# How do you use the quotient rule to find the derivative of y=tan(x) ?

##### 1 Answer
Mar 6, 2018

Kindly refer to the Explanation.

#### Explanation:

$\text{The Quotient Rule for Differentiation : } \left(\frac{u}{v}\right) ' = \frac{v u ' - u v '}{v} ^ 2$.

$\therefore \frac{d}{\mathrm{dx}} \left(\tan x\right) = \left(\sin \frac{x}{\cos} x\right) '$,

$= \frac{\cos x \cdot \left(\sin x\right) ' - \sin x \cdot \left(\cos x\right) '}{c s x} ^ 2$,

$= \frac{\cos x \cdot \cos x - \sin x \left(- \sin x\right)}{\cos} ^ 2 x$,

$= \frac{{\cos}^{2} x + {\sin}^{2} x}{\cos} ^ 2 x$,

$= \frac{1}{\cos} ^ 2 x$.

$\Rightarrow \left(\tan x\right) ' = {\sec}^{2} x$.