differentiate the function g(x)=In(xe^-2x)

Question

Please help me

Answer 1

The derivative will be easier to compute if we first simplify the function:

 

g(x) = ln(xe^-2x) = lnx + ln(e^-2x)

 

                      = lnx -2x

 

So, g'(x) = 1/x - 2 

Answer 2

You can also use the product rule and chain rule to find the derivative.

 

 

g'(x) = [e^-2x - 2xe^-2x] / xe^-2x

 

g'(x) = (1 / x) - 2