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

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

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

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

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