# What is the derivative of #(arctan x)^3#?

##### 1 Answer

Apr 11, 2017

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

#### Explanation:

By the chain rule we have:

# d/dx (arctanx)^3 = d/dx arctan^3x #

# " " = 3arctan^2x* d/dx (arctanx) #

And:

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

And so:

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