posted by Janet .
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.
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)
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
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?
Yes, if f"(x) replaces f'(x) on the left and f' replaces f on the right.
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.