Derivative?

[caitlynnora]

Find y" for y=2sin(y)+2x
Is it just y"=-2sin(y)? I got that by taking the first derivative of 2sin(y) to get 2cos(y), then took the derivative of that to get -2cos(y). Since it just wants y" does the 2x not matter/disappear?
Thanks!

 

[daon2]

Find y" for y=2sin(y)+2x
Is it just y"=-2sin(y)? I got that by taking the first derivative of 2sin(y) to get 2cos(y), then took the derivative of that to get -2cos(y). Since it just wants y" does the 2x not matter/disappear?
Thanks!

You will need the chain rule for the first derivative, and the chain rule and product rule for the second derivative. To show you why, let y=f(x). Then you're looking for f''(x) given

\(\displaystyle f(x)=2\sin(f(x))+2x\)

To start you off:

\(\displaystyle f'(x) = 2\cos(f(x))\cdot f'(x) + 2\)

Now you could, from here, solve for y'=f'(x), or you could continue taking the derivative of both sides and then solve for f''(x)