Question

What is the derivative of `f(x) = (x^3-x^2)/(lnx^2+lnx)`?

Answer 1

the first derivative

`f' (x)=((3x^2-2x) lnx^3 -3x^2 +3x)/(ln x^3)^2`

Explanation:

from the given

`f(x) = (x^3 -x^2)/(ln x^2 + ln x)=(x^3 -x^2)/(ln x^3)`

`f' (x)=((ln x^3)(3x^2-2x)-(x^3-x^2)(3x^2/x^3))/(ln x^3)^2`

which simplifies to

`f' (x)=((3x^2-2x) lnx^3 -3x^2 +3x)/(ln x^3)^2`