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

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Answer 1 · 2018-03-29T23:54:24

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

#f(x)=(arctanx)^3#

We can find the derivative #f'(x)# using the chain rule.

#f'(x)=3(arctanx)^2*color(red)(d/dxarctanx)#

The derivative of #arctanx# can be found on most tables that list derivatives of trigonometric functions.

#d/dxarctanx=1/(1+x^2)#

#f'(x)=3(arctanx)^2*color(red)(1/(1+x^2))#

#f'(x)=3((arctanx)^2)/(1+x^2)#