# How do you differentiate #f(x)=tan(lnx) # using the chain rule?

##### 1 Answer

Feb 16, 2016

#### Explanation:

The **chain rule** states that

#d/dx(f(g(x))=f'(g(x))*g'(x)#

First, we must know that the derivative of **chain rule** specific to tangent functions:

#d/dx(tan(x))=sec^2(x)#

#=>d/dx(tan(g(x))=sec^2(g(x))*g'(x)#

So, if we are differentiating the function

#f'(x)=sec^2(ln(x))*d/dx(ln(x))#

We must now know that the derivative of

#f'(x)=sec^2(ln(x))*1/x#

#f'(x)=sec^2(ln(x))/x#