# How do you find the derivative of the function: #(arctan(6x^2 +5))^2#?

##### 1 Answer

Jan 23, 2016

#### Explanation:

This will require a little chain rule.

The first issue is the second power, which can be dealt with as such:

#f'(x)=2arctan(6x^2+5)d/dx[arctan(6x^2+5)]#

Now, we must deal with the

#f'(x)=2arctan(6x^2+5)*(d/dx[6x^2+5])/((6x^2+5)^2+1)#

Simplify:

#f'(x)=(2arctan(6x^2+5)*12x)/((6x^2+5)^2+1)#

#f'(x)=(24xarctan(6x^2+5))/((6x^2+5)^2+1)#