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

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Answer 1 · 2015-11-25T12:47:05

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

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

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