Question

Find the derivative of the following function:
f(x) = $\frac{x}{1+tanx}$

Answer 1

Here $f\left(x\right)=\frac{x}{1+tanx}$

$\therefore f^{\prime }\left(x\right)=\frac{d}{dx}\left[\frac{x}{1+tanx}\right]$

$=\frac{(1+tanx)\frac{d}{dx}\left(x\right)-x\frac{d}{dx}(1+tanx)}{(1+tanx{)}^2}$

$=\frac{(1+tanx)\left(1\right)-x\left(se{c}^{2}x\right)}{(1+tanx{)}^2}$

$=\frac{1+tanx-xse{c}^{2}x}{(1+tanx{)}^2}$