1. ## Differentiation

I need help differentiating the following. I am not sure if what I have done is correct.

1. $\frac{d}{dx}\frac{1}{1+\sin(\cos x)}$

$=\frac{1}{[1 + \sin(\cos x)]^2}[\cos(\cos x)\sin x]$

2. $\frac{d}{dx} \log (1 + \sin(1 + \tan x))$

$= \frac{1}{1 + \sin(1 + \tan x)}\cos(1 + \tan x)\sec^2 x$

Could someone tell me if what I have done is correct or not.

2. correct