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Maths Derivatives & Calulus

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Maths Derivatives & Calulus
1) Find d^2y / dx^2 given that y^3 - x^2 = 4 2)If y = xª + ( 1 / xª ) , prove that x^2 . y'' + xy' – a^2 . y = 0 3) Find dy/dx for the following function. cos ( x - y ) = ( y ) ( 2x + 1 ) ^3 4)Find the values of A and B that make f(x) differentiable at x = 0 f(x) = A + 2x...

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

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

Maths Derivatives
If y = x ^ n + ( 1 / x ^ n ) prove that ( x^2y'' ) + ( xy' ) - ( n^2y ) = 0

Maths
Find the derivatives of these: f(x)=√

Math-Derivitives
if f(x)=x^3+5x, then f'(2)= if f(x)=cos(2x), then f'(pi/4) derivatives and anti derivatives please help

maths
find the maximum valu of any of the function without using derivatives 16x+8x+7

calculus
find the second-order 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

Math - Calculus 1
Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator: (1.1)^4 - (1.1)^2

calulus
lim tanx - x x->0 x^2

Calculus: Derivatives
I'm having trouble understanding what derivatives in calculus (instantaneous speed) is. Can someone please explain it to me, or provide some easy links to learn from? Thanks!

Calulus 2
Solve the differential equation: dy/dx = y^2 + y

Calulus
At what interval is 2x^3+0x^2-54x+6 increasing?

math
math question from applications of the derivatives. maths formula: V = 4/3(pi)r^3 dV = 4(pi)(3r^2) = 4(pi)r^2 But I don't understanding that how to get (3r^2) ?

Pre calulus only 15 min left HELP!
((ln(x))^1/2)/(ln(x^1/2))=6 solve for x

Calulus
Fundamental Theorem of Calculus 1. (4e^x-3)dx plus the number in x (6,1)

Calulus
[(5.2)^x (5.2)^-7]/(5.2)^-5 That whole thing is (5.2)^9 But I have no idea how to find the exponent x?

Calculus (Derivatives)
What is the derivative of the this functon? g(x) = -500/x, x cannot equal 0. I know that in order to fnd the derivative I need to put the function into the equation for evaluating derivatives as limits. lim as h -> 0 (f(x+h) - f(x))/h I did this, but I am having ...

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.

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 f''''(x) = 0.5 e^x - 0...

Calulus
Find f'(x): f(x)=(x^2-3x)/x^2 A. 2x-3/x^2 B. 2x-3/2x C. 1-(3/x) D. 3/x^2 E. None of these I can put it into the division rule for the derivative but get confused when I'm simplifying.

Maths Calculus Derivatives & Limits
Using the definition of the derivative evaluate the following limits 1) Lim h---> 0 [ ( 8 + h )^1/3 - 2 ] / h 2) Lim x ---> pi/3 ( 2cosx - 1 ) / ( 3x - pi)

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 my question. Do I need...

math derivatives
An architect is designing a rectangular building in which the front wall costs twice as much per linear metre as the other 3 walls. The building is to cover 1350 m2. What dimensions must it have so that the costs of the walls is a minimum? write a formula using derivatives

Calculus/Derivatives
In addition, can you walk me through how to get the derivatives for these 2 statements, too? a) y = x^5/3 - 5x^2/3 b) y = (the cubed root of the quantity) [(x^2 - 1)^2] Hi there. I need to find the first derivative of this statement. y=x(x+2)^3 I tried the chain rule, but I ...

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.

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 outside and inside.

Calulus
Given \displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a - \frac{b\pi^2}{c}, where a, b and c are positive integers and b and c are coprime, what is the value of a + b + c?

Calulus
Solve the triangle.Round lenghts to the nearest tenth and angle measurements to the nearest degree. B = 43 C = 107 B = 14

Derivatives
Find the derivatives of: 1. H(x)= sin2xcos2x The answer given is 2cos4x. My question is, how in the world did they get that!? Shouldn't the answer at least contain the sin function, either negative or positive seeing as it's the derivative of cos? Also, which rules are ...

Calulus Completely lost
Find the indicated one-sided limit, if it exists 1.lim f(x) and lim f(x), where x->0^+ x->0^- 2. f(x) = [2x if x is less than 0] [x^2 if x is greater than or equal to 0]

calulus
A plane flying at a constant rate of 200km/hr. What is the distance travelled by the plane 3mintues after it passes the observation point.

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)

calulus
The volume of the solid obtained by rotating the region enclosed by y=x^2 y=2x about the line x=2 can be computed using the method of disks or washers via an integral The volume is V

Calulus
Use the Midpoint Rule with n =3 to approximate the integral ç−1−8(10x−9x2)dx

Help- Calulus
A. If the focal length of the convex lens is supposed to be 5 cm, and if the image is formed 7 cm from the lens, find the distance, p, from the lens to the object. (It’s not necessary to simplify your answer.) Equation: 1/p + 1/q = 1/f

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' = [4(x+1)^(1/2)-4x]/[2(x+1)^(1/2)(x+1)] y' = (2-4x)/(x+...

calulus
a particle is moving along the cure y=sqrt x. as the particle passes through the point (4,2), its x-coordinate increase at a rate of 3 cm/s. how fast is the distancefrom the particle to the origin changing at this instant?

Calulus
You have 300 square feet of wood you will use to construct a rectangular shed with a square base and top. What is the maximum volume of your shed? Optimization Question

Maths Calculus
We want to build a rectangular cardboard box with no top and of given volume V using the least quantity of cardboard. Find the length of the box's edges by fnding the minimum of the total surface function. Verify that the point you found is indeed a minimum applying the second...

Calculus
What is wrong with the following reasoning??? f(x) = 2^x f'(x) = x[2^(x-1)] Although n x^(n-1) is the derivative of x^n, you cannot apply similar rules when x is the exponent and the number being raised to a power is a constant. The derivative of b^x, where b is a constant, is...

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 set them up for the ...

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 set them up for the ...

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 set them up for the ...

Maths Calculus Derivatives
Find the first derivative for the following functions 1) f(x) = sin(cos^2x) cos(sin^3x) 2) f(x) = ( tan 2x - tan x ) / ( 1 + tan x tan 2x ) 3) f(x) = sin { tan ( sqrt x^3 + 6 ) } 4) f(x) = {sec^2(100x) - tan^2(100x)} / x

calculus
derivatives. f(x)=(1/-7x^12) f'(2)=? f'(-1)=?

Math-Derivatives!!!
-4x^4 x^1/2+(-7/(x^2 x^1/2))

Derivatives ~ Calculus
If dy/dx = (1 + x)/(xy), x>0, and y=-4 when x=1, then when x=3, y= what?

derivatives
Applications of derivatives A rectangle has its base on the x axis and its upper two vertices on the parabola y=12 - x^2. What is the largest area the rectangle can have, and what are its dimensions. Support your answer graphically. Thanks. Well, the parabola is symettric ...

calulus
The top and bottom margins of a poster are 8 cm and the side margins are each 6 cm. If the area of printed material on the poster is fixed at 380 square centimeters, find the dimensions of the poster with the smallest area. find the width and height

Calculus
Compute the derivatives of : f(x)= x^7 + 7^x+ 7^7

Calculus-derivatives
Determine h'(x) for h(x)= [x/(1-x)]^2

Derivatives
differentiate and simplify y= (e^x - 1) / x^2

calculus
Anti-Derivatives 2x^6-x^3/x^2

Math derivatives
Let f(2)=3, g(2)=4, f'(2)=5, g'(2)=6, f'(3)=7, g'(3)=8, etc. find (f∘g)′(2)

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) = 1/(x+2) I tried to just ...

Calulus
Hi there I need help with one of the problem from my homework package. This week for my calculus class, we were learning how to do partial derivative and finding the tangent of the plane. So I do not know how to approach this problem. Please help me by how to derive this ...

Derivatives
What is f ''(x) and f ''''(x) of f(x)= e^-x^2 f"(x) = -e^-x^2(2x) F""(x)= -2e^-x^2 + 2xe^x^2 and also what is integral [0 to 2] f(x) dx

Calc
What are the derivatives? Thanks a) y = log(base2)(4-9x) b) y = x^(8x)

calc
What are the first and second derivatives of y = (1/x^2)-(1/(x-2)^2)?

calculus
find the derivatives F(x)=8ln(x^5-2x)

derivatives
How do you find the derivative of (6 csc x)/x?

derivatives
How do I find the 2nd derivative of x^(-1/15)

Calc
What are the first and second derivatives of y= x-3x^(1/3)

Calc
What are the first and second derivatives of y= x^(2/3) * (2.5 - x)

Calc
what are the first and second derivatives for y= x* (4-x^2)^1/2

calc
what are the first and second derivatives for y= x* (4-x^2)^1/2

calc
What are the first and second derivatives of y= x^(2/3) * (2.5 - x)

calculus derivatives
Please confirm: {(5x+2)^4/x^2-3x+1)^3}= 20(5x+2)^2(x^2-3x+1)^3 -3x^2(5x+2)^4 (x^2-3x+1)^2/(x^2-3x+1)^6

calculus
Find the derivatives of the functions k(x)=(x^3+e^x)^4

Derivatives
Find the derivative of xsecy+y^5=5x^3-7

Calculus Graph help!!!
I need help with a calulus graph and figuring out its equation but it wont let me post the picture of the graphs here. so will someone who understands Calculus and their graphs super well please email me k m k underscore horse lover at hot mail dot com. no spaces and an actual...

Calc--derivatives
find the der of y= x^(lnx) thanks

Calculus (derivatives)
Find the derivative of cos^2(4x)

calculus
find the derivatives 1. y=sin^3(2x)(cos2x)

calculus
find the derivatives 1. y=sin^3(2x)(cos2x)

calculus
derivatives: 2. cos teta/ 1+sin^2

Derivatives
Find the derivative of g(t)=8t^2+9t at t=1 algebraically... g'(1)= _________

trig derivatives
How do I find the derivative of 6 + 8cosx?

derivatives
how do u find the derivative of (csc x)^7 -cos 4x???

Math
Find the derivatives of the function g(t)= cosh^3 t.

math
what is meanning frechet and gateaux derivatives

Calc Derivatives
Find the critical points of (4x-3)/(3x^(1/2))

Math derivatives
Develop a rule for the following: Dx[f(x)g(x)/h(x)]

Math Derivatives
Find f''(2) of function f(x)=xsin(pi/x)

calculus
Find the derivatives of the following function: i)y=-3x^-3 +2x^-2 + x-2

Calulus
Consider the following function. f(t) = 3t2 − 3 (a) Find the average rate of change of the function below over the interval [3, 3.1]. (b) Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. (at t = 3) (at t = 3.1)

Econ/Math Derivatives
Find the derivative of the quotients: y=4X/(X-3)

Calculus
Find a formula for the derivatives of the function m(x)=1/(x+1) IS the answer -1/(x+h)(x+h+1)

calculus
derivatives: 3. y= cot^3(2/x) 4. y= csc^5 (1-t+3t^2) 5. y=sec(5x)/tan3x

Calculus(derivatives)
f(x)=7cosx+6tanx, find f'(x)and f'(5pie/4)

Calculus (derivatives)
find the slopes at the indicated points y = 3 + 5x - 3x^3 (0,3), (1/2, 41/8), (2,-11)

Anti-Derivatives
find the antiderivative of f(x) = x^3(x-2)^2 Someone help me please!

calc
find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2

math (2)
Find the first partial derivatives of the function. f(x,y,z) = xe^(y/z) a. fx = ? b. fy = ? c. fz = ?

math (2)
Find the first partial derivatives of the function. f(x,y,z) = xe^(y/z) a. fx = ? b. fy = ? c. fz = ?

math
Z=square root of (x^2+y^2) + xy Find the partial derivatives: x, xx, y, yy, xy. Thanks.

calculus
Z=square root of(x^2+y^2) + xy Find the partial derivatives: x, xx, y, yy, xy. Thanks.

Calculus
I get mixed up when graphing derivatives. If I'm given the graph of f how do I get f' and f"?

Calculus, derivatives
The curve is given by x^2+2r(sqrt(y))=xy What is dx/dr when y is constant?

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