# What is the derivative of sin^2x/cosx?

May 28, 2018

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

#### Explanation:

$f \left(x\right) = \frac{{\sin}^{2} x}{\cos} x$

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

$f ' \left(x\right) = \frac{2 \sin x {\cos}^{2} x + {\sin}^{3} x}{\cos} ^ 2 x$

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

The quotient rule is given by:

$f \left(x\right) = \frac{u}{v}$

$f ' \left(x\right) = \frac{v u ' - u v '}{v} ^ 2$