
math
I studied derivatives before, but kind of forgot them all, is there a website that gives me an overview of derivatives. What is first and second derivatives, how to find it, all the derivative rules and so on... thank you
asked by Sam on October 9, 2008 
convert derivatives of x,y,z, to r, Ɵ,z
convert derivatives of x,y,z, to r, Ɵ,z with chain rule? I want provment rules of converting rectangular derivatives to cylindrical derivatives and and also cylindrical to spherical.I know the rules but I cant prove EQUATIONS.thx alot
asked by parsa on December 1, 2011 
Calculus
Find the outside and inside functions of the following to find their derivatives: 1) sqrt(2x+9) 2) cos(cos(x)) 3) tan(x) I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would be considered the
asked by Robin on June 18, 2013 
calculus
find the secondorder partial derivatives of f(x,y)=x^3 + x^2y^2 + y^3 + x+y and show that the mixed partial derivatives fxy and fyx are equal
asked by maggie on March 7, 2012 
Calculus
show that the curves r=asin(è) and r=acos(è) intersect at right angles. can you show that the derivatives for each are the negative reciprocal of each other? That is the key. i need more info..i know how to find the derivative...but how will that prove
asked by Amy on April 5, 2007 
Math  Calculus 1
Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator: (1.1)^4  (1.1)^2
asked by James on October 7, 2016 
Calculus
Okay so I have a question on my assignment that says: You are given that tan(y) = x. Find sin(y)^2. Express your answer in terms of x. I know its derivatives, and I've tried taking the derivatives of both etc, and got them both to come out as cos(y)^2,
asked by Tracy on October 21, 2006 
MathDerivitives
if f(x)=x^3+5x, then f'(2)= if f(x)=cos(2x), then f'(pi/4) derivatives and anti derivatives please help
asked by AdrianV on March 23, 2010 
calculus
a)find the first partial derivatives of f(x y)= x √1+y^2 b)find the first partial derivatives of f(x,y)= e^x ln y at the point (0,e)
asked by maria on March 11, 2012 
Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2  x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = 2x fy = 2y gx = 0.5x gy = 2y And
asked by Justin on December 11, 2016 
Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2  x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = 2x fy = 2y gx = 0.5x gy = 2y And
asked by Justin on December 10, 2016 
Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2  x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = 2x fy = 2y gx = 0.5x gy = 2y And
asked by Justin on December 9, 2016 
Calculus
Hi~ Thank you for your help! I was trying to work on a problem about Taylor series, but i don't think im approaching the problem the right way. I have to find the fifth order Taylor polynomial and Taylor series for the function f(x) at x = 0. f(x) =
asked by KIKSY on March 7, 2011 
Calculus
Just got through with derivatives, power rule, and chain rule. I am supposed to find the first and second derivatives of the function. y = 4x/√x+1 and y = cos^2(x) y' = [(x+1)^(1/2)(4)][(4x)(1/2(x+1)^(1/2))(1)] y' =
asked by Justin on September 26, 2015 
Maths
Find the derivatives of these: f(x)=√
asked by alexis on November 13, 2012 
calculus
In dire need of help with derivatives. if f(x)=(x2+3x+6)3, find f'(x) if f(x)=3^1/2 / t^5 (square root of three divided by t to the 5th power), find f'(x) If f(x)=(3x+4)^–1 , find f(x) .
asked by michael on October 22, 2009 
calculus
Let f be a function that has derivatives of all orders for all real numbers. Assume f(0)=5, f'(0)=3, f''(0)=1, and f'''(0)=4. Write the thirddegree Taylor polynomial for h, where h(x) = integral of f(t)dt from 0 to x, about x=0 for this part, I got
asked by Meredith on March 16, 2007 
calculus
Find the derivatives of the functions k(x)=(x^3+e^x)^4
asked by Joe on February 11, 2013 
calculus quick question
g(x)= sqrt(14x^2) Can someone help me find the first and second derivatives please!
asked by dt on December 2, 2012 
calculus
find the derivatives F(x)=8ln(x^52x)
asked by melissa on April 6, 2011 
calculus
Find the derivatives of the following function: i)y=3x^3 +2x^2 + x2
asked by jayblaze on May 31, 2017 
Math
HELP DERIVATIVES!!!!!!!!!!!!! if h(x)=f[f(x)] use the tables for f and f' to find the value of h'(1) X f(x) f'(x) 1 3 2 2 1 5 3 6 7
asked by Ke$ha on December 26, 2016 
calculus
find the first and second derivatives for 3x^44xy^2+7=2y
asked by jack on October 14, 2015 
Calculus
Find all first partial derivatives: f(x,y)=e^(xy)cosx
asked by Elyse on May 31, 2013 
calc
find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2
asked by Jake on February 5, 2013 
math (2)
Find the first partial derivatives of the function. f(x,y,z) = xe^(y/z) a. fx = ? b. fy = ? c. fz = ?
asked by Mia on May 1, 2014 
Calculus  HELP plz!
Find all of the first partial derivatives of f(x,y,z)=arctan y/xz
asked by Sara on June 2, 2013 
calculus
find the derivatives 1. y=sin^3(2x)(cos2x)
asked by gen on January 4, 2011 
calculus
Find the first and second derivatives of the function. h(x) = sqrt x^2 + 1
asked by Vishnu on October 14, 2008 
math (2)
Find the first partial derivatives of the function. f(x,y,z) = xe^(y/z) a. fx = ? b. fy = ? c. fz = ?
asked by Mia on April 30, 2014 
Math
Find the derivatives of the function g(t)= cosh^3 t.
asked by Joe on October 9, 2012 
calculus
find the derivatives 1. y=sin^3(2x)(cos2x)
asked by gen on January 4, 2011 
Calculus
Find the first and second derivatives of the given functions. y=¡î(x©÷+1) y'=x(x©÷+1)^(1/2) y"=[1(x©÷+1)^(1/2)][(1/2)[(x©÷+1)^(3/2)](2x)(x)] y"=[(x©÷+1)^(1/2)][(x©÷)(x©÷+1)^(3/2)] Is the second derivative right?
asked by sh on November 10, 2009 
trig
I need help finding derivatives and antiderivatives. Given: f(x),find f'(x) 1. f(x)2x^6 2. f(x)= 3x +7 3. f(x)= 3x^2  5x 4.f(x)= 1/2x^2  x + 4
asked by Anna on January 12, 2012 
Calculas
Can someone please walk me through the steps for the following Partial derivatives problems: f(x,y) = x^7  8y  3, find x and y f(x,y) = 7 / 5x+4y, find x and y
asked by Annette on June 11, 2008 
Calculus
Find a formula for the derivatives of the function m(x)=1/(x+1) IS the answer 1/(x+h)(x+h+1)
asked by George on September 13, 2008 
calculus
Find all first and second partial derivatives of z with respect to x and y if x^2+4y^2+16z^2−64=0.
asked by andre on August 24, 2016 
Maths
Find the first and second derivatives of the following function: f(x)=7cosx+sin2x
asked by Amilia on November 20, 2017 
math
Z=square root of (x^2+y^2) + xy Find the partial derivatives: x, xx, y, yy, xy. Thanks.
asked by jean on September 24, 2014 
math
Find the derivatives of the following functions. 1.F (x)cotx 2.f (x)=sin (x2+2)
asked by samet on May 31, 2017 
calculus
Z=square root of(x^2+y^2) + xy Find the partial derivatives: x, xx, y, yy, xy. Thanks.
asked by jean on September 24, 2014 
Differential Euation
How do you find the primes denote derivatives with respect to x. Such as xy'+ 5y= 7x^2, y(2)= 5
asked by Danielle on February 15, 2012 
science
find derivative of f(x)=1/sqx^2+1 by using the definition of derivatives
asked by ibk on March 10, 2012 
Calculus
Find f(39)(x). f(x)=ex It gives no options and I'm so bad at high derivatives
asked by Twixx on January 17, 2019 
differential calculus
use the product rule to find the derivatives of the given function y=(3x^28)^2
asked by ash on April 30, 2011 
Calculus
If F(x)=f(g(x)h(x)), where g(3)=5, h(3)=4, g'(3)=3, h'(3)=1 and f'(1)=10, find F'(3). I know how to do derivatives and all, but I rlly can't figure this question out
asked by Aa on August 17, 2016 
math
Find the first order partial derivatives. z=ln(xysqrt(x^2y^2)
asked by jay on November 23, 2015 
Calculas
Can someone walk me through the following questions: Partial Derivatives f(x,y) = x^7 8y 3 find x and y f(x,y) = 7 / 5x + 4y, find x and y
asked by Annette on June 11, 2008 
calculus
find the partial derivatives du/dx, du/dy and du/dt. u= root (r^2+s^2, r = y + x cos(t), s = x + y sin(t);when x = 0, y = 2, t = 2
asked by Ramesh on October 10, 2011 
Math(Please help)
f(x,y)=x^2 e^2x lny (2,1) I need to find the partial derivatives with respect to x and y. I have not idea how to do this especially with the (2,1).
asked by Hannah on April 29, 2011 
math
find the derivatives, dy/dx for the folowing function : y=ln(cos(0.5)+(sin(x^2+3))^1/3)
asked by deel on August 25, 2012 
calculus
Just doing example questions to better understand. Find all first and second partial derivatives for the function u= xy^2+x^2y
asked by Todd on April 23, 2012 
maths
find the maximum valu of any of the function without using derivatives 16x+8x+7
asked by sandeep on June 26, 2014 
Calculus AB/BC
What's the purpose of finding derivatives? I don't understand why you would need to find a derivative, which is the tangent of the slope of a point on a graph, to find something like "How far did Bob fall". Confusing. Please help. Thank you!
asked by Dave on November 2, 2017 
Calc 3
Find all partial derivatives? v = (xy)/(xy) vxx= vxy= vyx= vyy=
asked by Becky on September 20, 2012 
math
find the derivatives, dy/dx, for the following functions : y=(1+sin^2{2 exp (3x)})^5y please help me to solve this assignment. thank's
asked by deel on August 20, 2012 
Pre Calc
f(x,y)=ln(5x^27y^3) Find ALL 2nd derivatives. fxx,fxy,fyx,fyy
asked by Sara on December 10, 2010 
calc 3
Find all partial derivatives? v = (xy)/(xy) vxx= vxy= vyx= vyy=
asked by Becky on September 19, 2012 
Math
Find the derivative of: ln(2x/x+1) the answer is 1/x(x+1) but i can't seem to solve it that far. ln [2x/(x+1)] = ln 2 + ln (x)  ln(x+1) Add the derivatives of each term and you get 1/x  1/(x+1) = [(x+1)  x]/[x(x+1)] = 1/[x(x+1)]
asked by Freddy on March 18, 2007 
Calculus
Find a formula for the derivatives of the function m(x)=1/(x+1) Please help.....Any assistance would be greatly appreciated.
asked by George on September 12, 2008 
Calc.
How do I deal with square roots and derivatives? Like: f(x)= Sqrtx....the derivative. find
asked by Derek on July 16, 2008 
calculus
find the following derivatives: f(x) = (2x+5)/(x^23) f'(x)= (2)*(x^2 3)(2x+5)*2x/(x^23)^2 is that correct??? f(x)= (lnx)(cos x) f'(x)= 1/x*sinx or do i have to use the product rule?? thank you.
asked by Dan on November 9, 2008 
Calculus
Find the derivatives of the function f(t)=cosh^2(4t)sinh^2(4t). Simplify your answer completely.
asked by Mike on March 3, 2013 
CALC
find the following derivatives: f(x) = (2x+5)/(x^23) f'(x)= (2)*(x^2 3)(2x+5)*2x/(x^23)^2 is that correct??? f(x)= (lnx)(cos x) f'(x)= 1/x*sinx or do i have to use the product rule?? thank you.
asked by Dan on November 9, 2008 
Calc/Precalc
Find the derivatives of 1. ln[(2x^3⋅2e^x)] 2. xy = cot(xy) 3. y = cos(x^3 + 27) I don't really know where to start with these. The answer is (3+x)/(x) for the first, y/x for the second, and 35. 3x^2 sin(x^3 + 27) but I have no idea how they got there.
asked by Heather on May 7, 2015 
math (8)
Find the secondorder partial derivatives of the function. f(x,y) = x^5 + x^2y^2 + y^4 + x + y a. fxx = ? b. fyy = ? c. fxy = ? d. fyx = ?
asked by Mia on April 30, 2014 
Maths
Find the derivatives of these: f(x)=(√(x))sinPix Also: f(x)=√(Cosx+sinx) Steps would be greatly helpful as I will be able to use them as reference. Thank you.
asked by Alexis on November 13, 2012 
math (7)
Find the secondorder partial derivatives of the function. f(x,y) = x^5 + x^2y + x + 5 a. fxx = ? b. fyy = ? c. fxy = ? d. fyx = ?
asked by Mia on April 30, 2014 
largest possible area
Again from applications of derivatives.. what is the largest possible area for a right triangle whose hypotneus is 5cm long, and what are its dimensions. Thanks a^2 + b^2 = c^2 3^2 + 4^2 = 5^2 Area of a triangle 1/2 base times altitude hint: base is 3
asked by Jen on November 18, 2006 
Calculus AB
Evaluate the following derivatives at the given points. Find the equation of the line tangent at each point. a) f(x)=ln(secx) @ x=pi/3 b) f(x)=(root(x+1))/(x1) @ x=0
asked by ireallyneedhelp on December 16, 2010 
Calculus
Hi, I am trying to find a closed form for the power series from n=2 to infinity of x^n/(n1)n. I'm not really sure how to do this I found the first and second derivatives which were x^(n1)/(n1) and x^n2. However, this didnt really seem to help much.
asked by Kira on August 2, 2017 
math/ calculus
full work out with explanation of this problem please we're working with derivatives and i don't understand it given h(x)= cotx/x find h'(pi/2)
asked by Angie on December 20, 2011 
Calculus
Find the derivatives of the function k(x)=sqrt(sin(2x))^3 I think I have the answer and was wondering if i had it correct k'(x)=2sin(x)^3+8sin(x)
asked by Joe on February 11, 2013 
Calculus grade 12
a) determine the derivative of y = sin2x b) determine the derivative of y = 2SinxCosx c) shoe that derivatives in parts a) and b) are equal d) explain why derivatives in parts a) and be should be equal.
asked by Julie on April 12, 2012 
cal
Finding Partial Derivatives Implicitly. Find dz/dx and dz/dy for 3x^(2)zx^(2)y^(2)+2z^(3)+3yz5=0 How would you type this in wolfram alpha calcultor to get the answer? Thanks,
asked by jay on March 15, 2014 
Calculus Derivative Taylor Series?
let f(x)= x/x1 find f'(x) f ''(x) and a formula for f ^ (n) * x. I found the first and second derivatives but do not know how to make a general equation for this. I have not learnt the Taylor or Maclaurin Series either. Thank you.
asked by Lisa on March 10, 2013 
calculus
Find a function f such that the curve y = f(x) satisfies y'' = 12x, passes through the point (0,1), and has a horizontal tangent there. I can use the antiderivatives to get y = 2x^3 + Cx + D but I don't know how to get C even though I know D = 1.
asked by asdf on November 29, 2012 
calculus
let f be the function f(x) = e^(2x^2) find the first four nonzero terms and the general term of the power series for f(x) about x = 0 i tried doing this problem but finding the derivatives gets way too complicated can anyone help??
asked by Anonymous on March 24, 2008 
engineering mathematic
give that z = f(x,y). use partial derivatives to find δz/δx and δz/δy for xe^xz + z(xy+1)^3sin x cos^2y=xy/z present your final answer in the simplest form.. please solve this problem....tq
asked by waklu on March 15, 2011 
2nd Order linear ODEs
I'm having trouble solving this problem: For the equation x^(2)y′′  xy′ = 0 , find two solutions, show that they are linearly independent and find the general solution. Hint: Try y = x^(r). I divided the equation by x^(2) first to simplify it, and
asked by Student on January 30, 2014 
math
so i am in precalculus, we need to graph the fuction using derivatives, maxima, intercepts and concavity. I am having trouble factoring cubics: for example: x^44x^3+16x > x(x^34x^2+16)Now what? That is without calculator, how do you find the roots?
asked by kathy on May 4, 2011 
Calculus
Evaluate the derivatives by implicit differentiation. Assume all letters represent constants, except for the independent and dependent variables occurring in the derivative. 𝑃𝑉^𝑐=𝑛𝑅𝑇 Find dP/dV
asked by Person on September 16, 2019 
Calculus
A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the yaxis. You must use calculus and clearly show your working, including any
asked by Daksh on July 18, 2014 
math
Find the first and second derivative of the function y=f(x)=x^3/(1(x^2)) Use the information about the derivatives to determine any local maxima and minima, regions where the curve iss concave up or down, and any inflection points
asked by ravinder on November 22, 2012 
Calculus
Find the first partial derivatives and evaluate each at the given point. Function w = 2x^2y − 6xyz + 10yz^2 Point (2, 5, −3) wx(2, 5, −3) = wy(2, 5, −3) = wz(2, 5, −3) =
asked by akash on November 17, 2015 
Calculus
Find the first partial derivatives and evaluate each at the given point. Function w = sqrt(5x^2 + y^2 − 4z^2) Point (2, −4, 2) wx(2, −4, 2) = wy(2, −4, 2) = wz(2, −4, 2) =
asked by Calculus Help on November 17, 2015 
Math
suppose u and v are functions of x that are differentiable at x=2 and that u(2) =3, u'(2) = 4, v(2) = 1, and v'(2) find values of derivatives at x = 2 (d/dx)(uv) = ? I would like to know how to set this up because I'm only used to getting problems that
asked by Amy on November 1, 2011 
Calculus
Find the four second partial derivatives and evaluate each at the given point. Function f(x, y) = x^3 + 2xy^3 − 9y Point (9, 2) fxx(9, 2) = fxy(9, 2) = fyx(9, 2) = fyy(9, 2) =
asked by Calculus Help on November 17, 2015 
Math
How do you find decreasing intervals of 6x^363x^2144x2? I found my increasing intervals from placing the derivatives i just can't seem to solve for the decrease
asked by Alessandra on November 4, 2014 
calculus
PLEASE HELP Find the first and second derivatives of the function. y = e^8ex. I keep getting y' = e^8ex * 8 and its wrong. how do you do this?
asked by nic on February 6, 2011 
derivative
find the first and second derivatives of (Ax^2+Bx+c)e^(3x) should i distribute e^3x into the prenthesis? or is there an easy way.... b/c when i distribute it i get a long answer..... for i get yp'=2Axe^3x+e^3xAx^2+Be^3x+e^3xBx+e^3x+ce^3x is that
asked by mary on November 19, 2008 
calculus  derivatives
can you please find the first 5 derivatives for: f(x) = (0.5e^x)(0.5e^x) f'(x) = ? f''(x) = ? f'''(x) = ? f''''(x) = ? f'''''(x) = ? thanks :) f(x) = (0.5e^x)(0.5e^x) f'(x) = 0.5 e^x + 0.5 e^x f''(x) = 0.5 e^x  0.5 e^x f'''(x) = 0.5 e^x + 0.5 e^x
asked by COFFEE on July 30, 2007 
Math
) Suppose that z=f(x,y)z=f(x,y) is defined implicitly by an equation of the form F(x,y,z)=0F(x,y,z)=0. Find formulas for the partial derivatives ∂f∂x∂f∂x and ∂f∂y∂f∂y in terms of F1,F2,F3F1,F2,F3. To enter your answer use F1, F2, F3 as the
asked by Usman on April 9, 2017 
Calculus
a) Find d/dm (x^4m^5 + y^3m +z^6) b) Find the first and second derivatives of: v = 3t^2 + 8t + 11 v' = v'' =
asked by Arin on February 5, 2015 
Math  Calculus
Problem solving with derivatives. Question: A piece of wire length of 30cm is cut into 2 sections. Each section is then bent into the shape of a square. Find the smallest possible value of the sum of the areas of the two squares.
asked by GZB on July 6, 2018 
Calculus
How do I solve this problem without integrals or derivatives? Find the distance traveled in 14 seconds by an object that is moving with a velocity of v(t) = 11 + 6cos t feet per second. A. 154.8204 B. 156.1704 C. 159.9436
asked by Anonymous on September 8, 2016 
Calculus
With y=f(x) (2x10)^1/2 having a virtual line joined at point Q from the origin (0,0), determine the coordinates of point Q that maximises the angle of vision of an observer, situated at the origin, following the movement of point Q along the curve. Note
asked by Jim on November 15, 2011 
calc
Find the derivatives of the following functions using the differentiation rules. f(x)=(x^32x^2+x+1)(sqrt(x)3x+9) I did: f'(x)=[x^32x^2+x+1][(1/2x^(1/2)3]+[x^(1/2)3x+9][3x^24x+1] which I got to be
asked by Anna on September 27, 2010 
Calculus
Find the derivatives of the function f(y)= sinh(sinh(7y).
asked by Jake on October 9, 2012 
Calculus
find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2 the sqrt is just over t.
asked by Mike on February 4, 2013
Pages
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868