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

1 Answer
Shwetank Mauria
Sep 18, 2016

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

Explanation:

In order to differentiate a function of a function, say #y, =f(g(x))#, where we have to find #(dy)/(dx)#, we need to do (a) substitute #u=g(x)#, which gives us #y=f(u)#. Then we need to use a formula called Chain Rule, which states that #(dy)/(dx)=(dy)/(du)xx(du)/(dx)#.

Here we have #y=(arctanx)^3#

Hence #(dy)/(dx)=d/(d(arctanx))(arctanx)^3xxd/(dx)(arctanx)#

= #3(arctanx)^2xx1/(1+x^2)#

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

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