Originally Posted by

**StarlitxSunshine** Use implicit differentiation to find the second derivative:

> $\displaystyle y+ sin y = x$

$\displaystyle dy/dx + cosy dy/dx = 1 $

$\displaystyle dy/dx (1+cosy) = 1$

$\displaystyle dy/dx = 1/1+cosy$

Up to this place all's right, but now you have to differentiate the right side, and get $\displaystyle \frac{d^2y}{dx^2}=\frac{\sin x}{(1+\cos x)^2}$.

I can't see from where that 3 in the power of the denominator in what you call "the answer" comes...

Tonio

$\displaystyle d^2y/dx^2 = /frac{1+cosy*0 - 1*siny*dy/dx}{(1+cosy)^2}$

$\displaystyle \frac{0-siny*dy/dx}{(1+cosy)^2}$

But the answer is

$\displaystyle \frac{siny}{(1+cosy)^3}$

What did I do wrong ?