Question

How do you differentiate `g(x) = xsqrt(1-e^(2x))` using the product rule?

Answer 1

`g'(x)=sqrt(1-e^(2x))-(x*e^(2x))/(sqrt(1-e^(2x))`

Explanation:

After the product and the chain rule we get

`g'(x)=sqrt(1-e^(2x))+x+1/2*(1-e^(2x))^(-1/2)*(-e^(2x))*2`
this simplifies to

`g'(x)=sqrt(1-e^(2x))-(x*e^(2x))/sqrt(1-e^(2x))`