Solve this following

If $y=(\tan x)^{\cot x}+(\cot x)^{\tan x}, \frac{d y}{d x}=(\tan x)^{\cot x} \operatorname{cosec}^{2} x(1-\log \tan x)$

$+(\cot x)^{\tan x} \cdot \sec ^{2} x[\log (\cot x)-1]$