# calculus derivative HELP!

18,009 results

### Calculus--> bobpursley

How do you get m=0? from taking the second derivative? does c=1? Can you check my work on how I get the derivative of R=M^2(c/2-m/3) NEXT R=1/2(CM^2)-1/3(M^3) NEXT dR/dM=CM-M^2. I checked in the back, and that was the answer for the first part of the equation. Isn't the ...

### Calculus - derivatives

Okay, I want to find the derivative of (x^x)^(x^x)... Well, I already went through the process of finding the derivative of just x^x (I used ln to do this). This is what I found... dy/dx = x^x(lnx+1) So now I want to find the derivative of (x^x)^(x^x) (using ln). This is what ...

### Calculus

I need to find the second derivative of y=x(x-1)^1/2. I found the first derivative is 2x-1/2(x-1)^1/2, if someone could check, but I am miserably stuck on the second derivative.

### Maths Calculus Derivative Integral - Urgent Please

Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = integral of 2x^2 (at the top) to x-5 (at the bottom) of square root of Sin(x)dx

### Calculus

1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^-1 x is 1/(|x|*sqrt(x^2 -1)). 4. Find the derivative of 2^(e^(sin x)). ...

### calculus

Please help with this. I need the first derivative of f(x)=4(x+squareroot (x(8-x)) and then the second derivative of this to show by the second derivative test that it is a local maximum. This is difficult to put into form here and I hope I have got it right. Many thanks.

### CALCULUS

what is the derivative of ln(x-1)? If you are studying the calculus of logarithms your question surprises me, since that is one of the most basic ones in that topic. in general if y = ln("anything") then y' = 1/"anything" * derivative of "anything" just apply this rule and let...

### CALCULUS HELP

Find the second derivative for the function 5x^3+60x^2-36x-41 and solve the equation F(X)=0 i got to the second derivative but what do we do next to be able to get one of these answers.. F(x) = 5x3+60x2−36x−41 1. derivative of F(x) with respect to x = 15x2+120x&#...

### Calculus

Suppose f(x) and g(x) are functions of x differentiable at x = 4. Given that f(4) = 3, f'(4) = -2, g(4) = 6, g'(4) = -4, find the value of each of the following. a. Derivative of f(x) * g(x) My answer: -27 b. Derivative of (f(x))/(g(x)) My answer: 1/12 c. Derivative of (g(x...

### calculus

Please help with this. I submitted it below and was asked to clarify by Henry (hope this is clearer and thank you). I need the first derivative of f(x)=4(x+ sqrt (x(8-x)).And then the second derivative of this to show by the second derivative test that it is a local maximum. ...

### Calculus (Help)

Also I would like to know how to set this problem up in finding the answer: Find the second derivative. y= sqrt(3x+4) Thanks, P.S. I tried taking 3x+4 and squaring it to the 1/2. I thought that might've been the same, then I took the derivative of that and got 1/2(3x+4)^(-1/2...

### calculus

Differentiate both sides of the double angle identify sin 2x= 2 sin x cos x to determine an identify for cos x. Find the first derivative, second derivative, third fourth, fifth, sixth, seventh and eighth derivative. Use the results to find the twelfth and fifteenth derivative...

### calculus

Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation)

### Calculus

Suppose f(x) and g(x) are functions of x differentiable at x = 4. Given that f(4) = 3, f'(4) = -2, g(4) = 6, g'(4) = -5, find the value of each of the following. a. Derivative of f(x) * g(x) My answer: -27 b. Derivative of (f(x))/(g(x)) My answer: 1/12 c. Derivative of (g(x...

### calculus

Find the first and second derivative - simplify your answer. y=x/4x+1 I solved the first derivative and got 1/(4x+1)^2 Not sure if I did the first derivative right and not sure how to do the second derivative.

### Calculus

Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x ã3x + 1 (3x + 1 is under the square root) 5...

### Applied Calculus

Find the first and second derivative of the function: x/(7x+10) Using quotient rule. This is part of my homework in the section named "Higher Order Derivatives". I am confused on getting the second derivative, as I found the first derivative to be 10/(7x+10)^2

### Calculus

Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x /3x + 1 (3x + 1 is under a square root(/) 5) ( f...

### Calculus

If I have a function f(x), and am given its derivative, f'(x): may I take it as a given that f(x) is an integral of f'(x). My reasoning is that 'undoing' the derivative gives me the derivative. Eg is 1/3x^3 an integral of x^2? Thanks.

### Calculus derivatives

f(a) = a + √a (a) Find the derivative of the function using the definition of derivative.

### Calculus 1

Find the derivative dy/dx for the following. Simplify your answer. y=(ln(x^2))/(x^3) I got (2/x x^3-3x^2 ln(x^2))/((x^3)^2) for the derivative is that correct? Or no?

### Calculus

Find the value of the derivative (if it exists) of f(x) = (x+3)^(4/3) at x=-3. So I got (4*(x+3)^(1/3))/3 for the derivative and 0 for the final answer.

### calculus

Calculate the derivative of the function. Then find the value of the derivative as specified. f(x) = 8/(x+2); f '(0)

### Calculus I

Find the derivative of y=ln((1+e^x)/(1-e^x)) I know that the derivative of y=ln(1+e^x) would be (e^x)/(1+e^x), but I'm not sure what to do with the 1-e^x on the bottom here. Can someone help please? Thanks!

### Calculus

R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? set it to zero, and solve for m. You get two solutions. Use the second derivative to see which one is the max. I get M=C. How do I go from there? What do ...

### Calculus

If P'(t)= [10(t+2)]/t. What is P(t)? It is asking for the derivative, and I am so lost! Because so far we haven't covered how to find the derivative of something so complicated. Any ideas? TY

### calculus

Use the function defined below to calculate the indicated derivative. f(t)= 4/(t^3)+3 what is f''(2) (second derivative) Need help!!

### Calculus

Use derivative formulas to find the derivative of the function. please show your work h(x)=10^3-25x^6+3x^15

### calculus

3. Plot f(x) =ln(x) and f’(x) = 1/x in your calculator. Remembering that the derivative of f(x) is the instantaneous rate of change of f(x) why does it make sense that 1/x is the derivative of ln(x)?

### Calculus Please check

Please check my answers and let me know if I did something wrong. Thank you! Find the partial derivative of x, and the partial derivative of y, then the partial derivative of x (1,-1), and the partal derivative of y (1,-1). f(x,y) = x^4 y^2 -x here is what I got @f/@x = 3x^3 y...

### Calculus

Find the derivative of the function using the definition of a derivative. F(x)=squareroot(1-3x) Please show work for understanding, thank you! :)

### calculus

Please help with this. I submitted it below but no one responded. I need the first derivative of f(x)=4(x+ then the square root to include (x(8-x)), then close bracket.And then the second derivative of this to show by the second derivative test that it is a local maximum. This...

### Calculus

Find the derivative of f(x)=x(1-4^x) f'(x)=(1-4^x)+ (-4^x)(ln-4)(-4)(x) ln can't be negative. Is the derivative correct?

### Calculus

Find the derivative of m(x)=1/(x+1) by using the definition of the derivative.

### Calculus derivative

find the slope m and an equation of the tangent line to the graph of the function f at the specified point. original: x^2/x+10 point: (3,9/13) After I found the derivative: (x+10)(2x)-(x^2)(1)/((x+10))^2 How do I get the slope? Should I put 3 into the derivative equation?

### Calculus

Show that the curves r=acos(è) and r=cos(è) intersect at right angles. can it be shown that the derivative of one is the negative reciprocal of the derivative of the other?

### Calculus Derivative

I'm trying to calculate the derivative of this: P= mv/ sqrt(1-v^2/c^2)where m and c are constants, and v depends on t. I know about the chain and product rules but I'm not even sure where to start. :/ Thank you for your help.

### Calculus

can sumeone plz help me find the derivative of (2x^2 - 12x -2) / ((x^2 + x - 2) ^ 2) thx a lot Use the following rule: derivative of u(x)/v(x) = [v du/dx - u dv/dx]/ v^2 In your case, du/dx = 4x - 12; dv/dx = 2 (x^2 + x -2)*(2x +1) v^2 = (x^2 + x - 2)^4 Put it all together

### calculus

Hello. I need help finding the open intervals of this equation: f(x)=3x^2-12 I already took the derivative of it by using the derivative test and I got 2,-2 as critical numbers

### calculus

Hello. I need help finding the open intervals of this equation: f(x)=3x^2-12 I already took the derivative of it by using the derivative test and I got 2,-2 as critical numbers

### calculus

For a function f(x) the derivative at x=2 is 5. Is the derivative of f(x) continuous at x=2? Thanks!

### calculus

Would the derivative of ln(x^2) be 1/x^2? and also the derivative of ln(2^s) be 1/2^s

### Calculus derivative

How do you do the derivative of a^x, for example, (3/4)^x Thank you for helping!

### calculus derivative HELP!

Find the derivative of: y=2sqrt(x)-(1/x)

### Calculus

let F(x) = f(2x) and suppose that the derivative of F(x) = x^(2). Find the derivative of f(2x).

### Calculus

Does my answer look correct? Find the derivative. 11, y= (e^3-e)(e+5)/6e my work: ((6e)(4e^3 + 15e^2 - 2e - 5) - (6)(e^4 + 5e^3 - e^2 - 5e))/ (6e)^2 Multiplied/divided everything through My answer: (10e^2 + 30e - 3)/ 18 I cant follow your work: I assume e is a derivative. (e^3...

### calculus

i need to use implicit differentiation to find the derivative: yx+y = 8 i keep getting y'=-1-y. i already know the derivative of this, by using explicit by simplification: y(x+1)=8 y=(8)/(x+1) y'= -(8)/(x+1)^2 how do i go about doing this the right way?

### Calculus

Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or second derivative rule ...

### Calculus

Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or second derivative rule ...

### Calculus

Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeroes of the graph of ...

### calculus

Could someone check my reasoning? thanx Find the derivative of the function. sin(sin[sinx]) I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the derivative of sin[sinx]. And multiply that by ...

### math

Let f be a real value function and x Î Df then 0 lim ( ) ( ) h f x h f x ® h + - when it exists is called A) The derivative of f at a B) The derivative of f at h C) The derivative of f at x D) The derivative of f at x = h

### Calculus

How would I go about finding the derivative of f(x)=ln(x)(7x-2)^3 first=ln(x) second= (7x-2)^3 Would I do first times the derivative of the second + second times the derivative of the first? If so, what is the derivative of lnx? I'm confused. Thanks for your help. --Cori

### College Calculus 1

We have to find the first and second derivative of f(x)=x^(2/3)(6-x)^(1/3) I have the first derivative as being (4-x)/(x^(1/3)(6-x)^(2/3)) And that I know is right. The second derivative is -8/(x^(4/3)(6-x)^(5/3)) I did all the work but I am not getting the right answer... I ...

### Derivative Calculus

I just need my answers checked. 1) Find the derivative. f(x)=3x^5/4 - 8/9x^9/8 + x^2 - 9x + 1 Answer: f’(x)= 15/4x^1/4 - x ^1/8 + 2x -9 2) Let f(x)= 7x^3 - 9x. Find f’(5) Answer: f’(x)=21x^2-9 f’(5)=516 3) Find the given limit by evaluating the derivative. lim h⇒...

### calculus

how do you find the derivative of (X^2(2+x^1/2))/x^4. I'm confused because of the exponents rules. please show me the steps in simplifying the exponents then taking the derivative.

### calculus

find the second derivative of F(x)=3e^-2x(^2) to find the inflection points. I am trying but I don't think I'm finding the first derivative correctly.

### Calculus

y= ln3x *e^2x^2 + sin5x^2 find the derivative. i know what to do. but what is the derivative of ln3x? I can plug it into the product rule then nd solve

### physics/calculus

can someone explain to me why the derivative and second derivative of this position vector r=ax+bty is r'=ax' +by'+ bty' ( why is there a by'...?) and r''=ax'' + cy' +cy' +cty'' ( why is there 2 cy' 's?

### Calculus (Global Max)

Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or second derivative rule ...

### Calculus

What is the derivative and second derivative of 3x/(x^2-4)

### calculus derivative

find the derivative of: y=(x/(x+1))^3

### Calculus Derivative

Find derivative: y= e^(x^x)

### Calculus

How do I use the product rule to solve these two questions. Much appreciated! xo Find the derivative for k(x) = (5x4 + 2)(3sin x) Find the derivative for m(x) = -ex cos x at x = 1

### Calculus

Hello I need help with this excersise of derivative of a inverse function. The excersise says: If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^-1 (9))'[the derivative of the inverse function evaluated in 9] . I don...

### calculus

find the derivative of f(x)=x^2sec^2(3x) also with g(x)=sqrt(cosxsecx) i get zero because cos and sec cancel each other out and derivative of a constant is zero... am i doing something wrong?

### Calculus

Decide if the following function f(x) is differentiable at x=0. Try zooming in on a graphing calculator, or calculating the derivative f'(0) from the definition. f(x) = x^4sin(2/x), if x is not equal to 0, and f(x) = 0 if x = 0. If it is differentiable, what is the derivative...

### calculus

If the hands on a clocktower's clock are 2ft and 3ft long, how fast is the distance between the tips of the hands of the clock changing at 9:20? I know that the derivative of the minute hand is pi/30 rad/min and derivative of the hour hand is pi/360 rad/min. what is the ...

### calculus

in a time of t seconds, a particle moves a distance pf s meters from it's starting point, where s=3t^2 Find the ave velocity between t =1 and t=1+h if.... a) h=.1 b)h+.01 c)h=.001 Which approximation is closest to the EXACT derivative at ...t=1? Estimate the exact derivative ...

### Calculus

I know the derivative of x is 1, but I'm having a hard time proving it with the limit definition of the derivative. I have... Lim delta x ->0 (x+ delta x)-(x)/delta x = 0 But I know the answer is 1. I don't understand what I am doing wrong

### Calculus

If x = t^2 + 1 and y = t^3, then d^2y/dx^2 = I know I can solve for t in terms of x and substitute that into y = t^3 and find the double derivative. I also know that I can take the derivative of x and y then divide dy/dt by dx/dt. Then take the derivative to get the answer. ...

### Calculus-verify

What is the second derivative of f(x) = 5/3x^(3) - x^(3/2) + 6? Second derivative of f(x) = 5/3x^(3) - x^(3/2) + 6 is f''(x)=10x + 3/(4sqrt of x)

### Calculus

Please help me. 1. Use the definition of the derivative to find f'(x), if f(x)=x^-2 2.Find the derivative of y=3t^5 - 5√t + 7/t

### calculus

You are given the following function. f(x)= (8+x)/(1-8x) (a) Find the derivative of the function using the definition of derivative. (b) Give the domain of the function. c) Give the domain of derivative of function?

### Calculus

I need help with finding first and second derivative--simplify your answer. Y=xtan(x) I solved first derivative xsec^2(x) + tan(x) I don't understand how to get the first...can someone show me the steps with explanation?

### calc

derivative of (x^3/6)+(1/2x)? i got (x^2/2)-(1/2x^2) is that correct? and then wut is the (F'(x))2?...meaning the derivative squred? if you meant (1/2)x^2 - 1/(2x^2) you are correct I don't think they are looking for the square of the derivative, but rather the second ...

### Differential Calculus

Determine all local extrema, concavity and inflection point/s for y = -2cos(x) in (0, 2Pi). Test by both First Derivative Test and Second Derivative Test and sketch the graph.

### Calculus - First Derivative

Original Equation: f(x) = e^(-x) - e^(-2x) Did I take the first derivative correctly? I seem to get undefined when I isolate for x to determine the extreme values? f'(x) = -e/ x + 2e/2x f'(x) = (-2ex + 2ex) / 2x^2

### Math:Calculus

Use the Fundamental Theorem of Calculus to find the derivative of g(x)=1/(1+t^5)dt in the interval 1 to x.

### Calculus Help STEVE

find y'' by implicit differentiation. 2x^3 + 3y^3 = 8 I got the first derivative as you but the problem was asking for second derivative by implicit diff. this is where i got confused. Thank you!!!

### Calculus

find the derivative of y= x^3+8/x+2 the / is meant to be a fraction bar, I am really really bad at finding the derivative of a fraction function, could you help by showing me exactly how, Thanks

### math, calculus 2

Use part 1 of the Fundamental Theorem of Calculus to find the derivative of g(x)= integrate from 9x to 4x of ((u+4)/(u-1))du

### math derivative please help

the derivative of 2x^e is zero right or no? do i have to use the log formula 2 x^e is x to the power 2.718.. It is not a constant and therefore the derivative is not zero. Use the formula for the derivative of x to a power that is constant (x^a). The formula for that may ...

### Calculus

Find the anti derivative of the following: 1. u^-2(1-u^2+u^4)du 2. (sqrt(x)+ 3/x - 2e^(x))dx The anti derivative symbol is in front of the equations. Also need help on find f(x) so that it satisfies f'(x) = 1+e^x+1/x and f(1) = 3+e. Please show steps so I can understand. Thanks.

### 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 ...

### Calculus

What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like? How would taking the derivative of the function in its original form look different when using log ...

### Calculus AP need help!

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. If f(x)= ∫(4,x^3)√(t^2+10) dt then f '(x).

### Calculus

1. is the derivative of the function f(x)=5e^(4x-9z) f'(x)= -25e^(4x-9z)? 2. Is the derivative of the function f(x)=e^(2x)-e^(-2x) f'(x)=2e^(2x)+2e^(-2x)? 3. If f(x)=e^-x^-1, would f'(2)=-1/4e^(1/4)?

### Calculus,Stationary Points,First derivative test

Good afternoon, I need a bit of help. So ive got my first derivative which is 6x^2-6x-12 and the stationary points ive found are x=-1 and x=2 at which points the value of the derivative is zero. So im attempting to classify the points. From my derivative tests the value of -2 ...

### Calculus

Find the derivative of the following function using the appropriate form of the Fundamental Theorem of Calculus. intergral s^2/(1+3s^4) ds from sqrtx to 1 F'(x)=?

### Calculus

Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative Please show me how u got this!!

### Calculus

find derivitive of 1/square root of x 1/square root of x = x^(-1/2) The derivative is -1/2 x^(-3/2) can you keep going on the problem to not have negative exponents? You can also use that the derivative of 1/f(x) is given by: -f'(x)/[f(x)]^2 If you take f(x) = sqrt(x) and use ...

### calculus

A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)sqrt(x+1)(<or=)10? B) So once that is found, then how can you prove that if 0(<or=)u(<or=)v(<or=)10, then 0(<or=)sqrt(u+1)(<or=)sqrt(v+1)(<or=)10? * calculus - Damon, Saturday, April 3, ...

### Calculus:check please

given: 1st derivative is 2(2-3x-2x^2)/(1+x^2)^2 (quotient rule) I've found the stationary points to be x=1/2 and x=-2 Am I on the right track? If so, I plan to plug in values to the L andR of them into the whole derivative so as to clasify them. Still on track? Thanks those ...

### Multivariable calculus

Hello, I have the next exercise about chain rule in multivariable calculus: I have to show that the differential equation: y(dz/dx)-x(dz/dy) = (y-x)z can be change to the equation: (dw/dv) = 0 using the new variables: u= (x^2)+(y^2) v = (1/x)+(1/y) w = ln(z)-(x+y) For that I ...

### Calculus

For 0 < x < PI/2, if y = sin(x)^x, then dy/dx is.. I understand that you can take the natural logarithm of both sides and then take the derivative but why can't I simply take the derivative of it and get.. dy/dx = x(cos(x))(sin(x))^(x-1). Thanks in advance :).

### calculus

1.) values of f(t) are given in the following table: t 0 2 4 6 8 10 f(t) 137 112 88 68 49 34 a. Does this function appear to have a positive or negative first derivative? Second derivative? * I think both derivatives are negative b. Estimate (f prime) f^' (2) and f^' (8) ...

### 12th Grade Calculus

Find d^2y/dx^2 by implicit differentiation. x^(1/3) + y^(1/3) = 4 I know that first you must find the 1st derivative & for y prime I got 1/3x^(-2/3) + 1/3y^(-2/3) dy/dx = 0 Then for dy/dx I got dy/dx = [-1/3x^(-2/3)] / [1/3y^(-2/3)] I think that from here I would use the ...

### Calculus

h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. For what values of a will h(x) have a relative maximum at x=1? So I found the derivative and got h'(x) = 1- asin(ax). Then I plugged in 1 for x and set the derivative equal to zero, so I have 1 - asin...