Question

Differential the following functions w.e.t.x:
$\frac{x\tan x}{\sec x+\tan x}$

Answer 1

$y=\frac{xtanx}{secx+tanx}=\frac{xsinx}{1+sinx}$

$\frac{dy}{dx}=\frac{(1+sinx)[sinx+xcoxx]-\left(xsinx\right)\left(cosx\right)}{(1+sinx{)}^2}$

$\frac{dy}{dx}=\frac{sinx+xcosx+si{n}^{2}x}{(1+sinx{)}^2}$

$\frac{dy}{dx}=\frac{sinx(1+sinx)+xcosx}{(1+sinx{)}^2}$