Question

How do you differentiate `g(x) = (2sinx -e^x) ( cosx-x^2)` using the product rule?

Answer 1

`g'(x)=2cos^2(x)-e^xcos(x)-2x^2cos(x)+x^2e^x-2sin^2(x)+e^xsin(x)-4xsin(x)+2xe^x`

Explanation:

using the product rule we get
`g'(x)=(2cos(x)-e^x)(cos(x)-x^2)+(2sin(x)-e^x)(-sin(x)-2x)`