# How do you find the derivative of # y = ln(secx)#?

##### 2 Answers

Apr 1, 2017

#### Answer:

See below

#### Explanation:

In order to differentiate this function, we must use the chain rule:

Informally, this means that if we have to derivate a composite function,

The function to derivate is

Apr 1, 2017

#### Answer:

#### Explanation:

We can also rewrite this using logarithm rules:

#y=ln(secx)=ln(1/cosx)=ln((cosx)^-1)=-ln(cosx)#

The derivative of

Thus,

#dy/dx=-1/cosx*d/dxcosx#

The derivative of

#dy/dx=-1/cosx(-sinx)=sinx/cosx=tanx#