# How do you find the derivative of f(x) = sin x + 1/2 cot x?

Jan 8, 2017

$f ' \left(x\right) = \cos x - \frac{1}{2} {\csc}^{2} x$

#### Explanation:

The terms in f(x) have $\textcolor{b l u e}{\text{standard derivatives}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(\sin x\right) = \cos x} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{and } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(\cot x\right) = - {\csc}^{2} x} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow f ' \left(x\right) = \cos x - \frac{1}{2} {\csc}^{2} x$