Posted by Janet on Wednesday, March 16, 2011 at 11:56pm.
Find the first and second derivative - simplify your answer.
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 - MathMate, Thursday, March 17, 2011 at 12:14am
The first derivative of 1/(4x+1)² is correct.
For the second derivative, you just have to differentiate the first derivative with respect to x.
You can use the chain rule, substituting u=4x+1, and differentiate 1/u² using the power rule.
=d(1/u²)du * du/dx
=-2/u³ * (4)
- calculus - drwls, Thursday, March 17, 2011 at 12:18am
y = x/(4x +1)
dy/dx = [(4x+1) - 4x]/(4x +1)^2
= 1/(4x +1)^2
OK so far
d^2y/dx^2 = -2(4x +1)^-3 * 4
- calculus - Janet, Thursday, March 17, 2011 at 1:09am
To solve the first step I used the equation
f'(x)=lim h-->0 f(x+h)-f(x)/h
Can I use this same formula to solve for the second derivative?
- calculus - drwls, Thursday, March 17, 2011 at 6:25am
Yes, if f"(x) replaces f'(x) on the left and f' replaces f on the right.
- calculus - Janet, Thursday, March 17, 2011 at 8:00pm
I plug in the numbers into the formula that I used, but I don't get the same answer.
Here's what I did, maybe you can tell me what I did wrong. (likely a dumb algebra mistake)
f"(x) = lim-->0 f'(x+h)-f'(x)/h
=(1/4(x+h)+1)^2 - (1/4x+1)^2/h
I can't figure out where I went wrong.
Answer This Question
More Related Questions
- Calc I - if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t...
- Calculus - I need help with finding first and second derivative--simplify your ...
- Calculus AB - I'm trying to find the second derivative of h(x)= x^2 + cos(kx) My...
- College Calculus 1 - We have to find the first and second derivative of f(x)=x^(...
- math - For what intervals is g(x) = 1/x2 + 1 concave down? (Enter your answer ...
- calculus - Please help with this. I need the first derivative of f(x)=4(x+...
- Applied Calculus - Find the first and second derivative of the function: x/(7x+...
- Derivatives- Math - Can someone explain how to find the derivative of : 1. y= 5...
- Calculus - I need to find the second derivative of y=x(x-1)^1/2. I found the ...
- calculus - Please help with this. I submitted it below but no one responded. I ...