How do you find the derivative of #y=tan(x)# ?
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.
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.
which is equivalent to: