Question

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

Answer 1

`g(x)=(e^(2x)−e^x)(x−x^2)`

Applying product rule,

`g'(x)=(e^(2x)−e^x)(x−x^2)' + (e^(2x)−e^x)'(x−x^2)`

derivative of `e^x` is `e^x`, therefore,

`=>(e^(2x)−e^x)(1−2x) + (2e^(2x)−e^x)(x−x^2)`