# How do you find the derivative of #y=tan(x)# ?

##### 1 Answer

This is a common identity which many people memorize, along with the derivatives of

It can be proven easily using two well-known trig identities and the quotient rule.

**Process:**

First recall from pre-calculus that

So, we can rewrite

Now, we differentiate, and apply the quotient rule:

We know that the derivative of

It should be clear that the numerator can be simplified using another trig identity.

Recall

Substitution yields:

which is equivalent to: