What is the derivative of this function #sin^3(x)cos(x)#?

1 Answer
Feb 28, 2017

Derivative is #3sin^2xcos^2x-sin^4x#

Explanation:

We use the product rule and chain rule here.

Product rule states if #f(x)=g(x)h(x)#, then #(df)/(dx)=(dg)/(dx)xxh(x)+(dh)/(dx)xxg(x)#

and according to chain rule if #y=f(u(x)# then #(dy)/(dx)=(dy)/(du)xx(du)/(dx)#.

Hence as #y=f(x)=sin^3xcosx#

#(df)/(dx)=3sin^2x xx cosx xx cosx+sin^3x xx(-sinx)#

= #3sin^2xcos^2x-sin^4x#