Question

What is the derivative of `f(x) = xcos^3(x^2)sin(x^2)`?

Answer 1

`(df)/(dx)=cos^3(x^2)sin(x^2)-6x^2cos^2(x^2)sin^2(x^2)+2x^2cos^4(x^2)`

Explanation:

We can use here product formula for three terms i.e.

if `f(x)=p(x)*q(x)*r(x)`, then

`f'(x)= p'(x)*q(x)*r(x)+p(x)*q'(x)*r(x)+p(x)*q(x)*r'(x)`

Hence for given function `f(x)=xcos^3(x^2)sin(x^2)`

`(df)/(dx)=1xxcos^3(x^2)sin(x^2)+x*(3cos^2(x^2)xx(-sin(x^2))xx2x)*sin(x^2)+xcos^3(x^2)xx(cos(x^2)xx2x)`

= `cos^3(x^2)sin(x^2)-6x^2cos^2(x^2)sin^2(x^2)+2x^2cos^4(x^2)`