# What's the derivative of #arctan(x^3/3)#?

##### 1 Answer

Feb 16, 2016

#### Explanation:

We can use the **chain rule,** which states that

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

In the case of an arctangent function, it will help to know that

#d/dx(arctan(x))=1/(x^2+1)#

When we apply this to the **chain rule,** we see that

#d/dx(arctan(g(x)))=1/((g(x))^2+1)*g'(x)#

When differentiating

#d/dx(arctan(x^3/3))=1/((x^3/3)^2+1)*d/dx(x^3/3)#

Through the power rule, we know that

#=1/(x^6/9+1)*x^2#

#=x^2/((x^6+9)/9)#

#=(9x^2)/(x^6+9)#