Does the derivative of f(x)=ln(e^2x)/(x^2-8) equal (2(x^2-x-8))/(x^2-8)

Answer 1

log(e^2x) is equal to 2x

Hence, the derivative, by applying the quotient rule becomes

f'=Numerator/Denominator

where Numerator=2*(x^2-8) - 2x*(2x) and Denominator=(x^2-8)^2

You can further simplify them as

f'=(-2x^2-16)/(x^2-8)^2

Best,

Davide