# How do you differentiate f(x)=x/cotx using the quotient rule?

Nov 24, 2015

$f ' \left(x\right) = \frac{x {\csc}^{2} x + \cot x}{\cot} ^ 2 x$

#### Explanation:

According to the Quotient Rule:

$f ' \left(x\right) = \frac{\cot x \frac{d}{\mathrm{dx}} \left[x\right] - x \frac{d}{\mathrm{dx}} \left[\cot x\right]}{\cot} ^ 2 x$

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

$f ' \left(x\right) = \frac{x {\csc}^{2} x + \cot x}{\cot} ^ 2 x$