Question

What is the derivative of `f(x)=e^(lnx^2)*lne^x`?

Answer 1

You should simplify first.

Please remember that `ln x` and `e^x` are inverse functions. This means that `ln e^x = x` and `e^(ln x) = x` hold.

With this knowledge, you can simplify as follows:

`f(x) = e^(ln x^2) * ln e^x = x^2 * x = x^3`

Therefore, the derivative is

`f'(x) = 3x^2`.