How do you find the derivative of # x^2*tan^-1 x#?

1 Answer
May 9, 2016

#(x^2)/(1+x^2)+2xtan^-1x#

Explanation:

Differentiate using the #color(blue)" product rule "#

• If f(x) = g(x).h(x) then f'(x) = g(x).h'(x) + h(x).g'(x)
#"---------------------------------------------------------"#
here #g(x)=x^2rArrg'(x)=2x#

and #h(x)=tan^-1xrArrh'(x)=1/(1+x^2)#
#"---------------------------------------------------------"#
Substitute these values into f'(x)

#rArrf'(x)=x^2 1/(1+x^2)+tan^-1x.2x#

#=x^2/(1+x^2)+2xtan^-1x#