Q 30. - Calculus

Question

Find the derivatives of each of functions in Exercises 17–44. In some cases it may be convenient to do some preliminary algebra.
$f\left(x\right)={\left(x^e\right)}^e$

Step-by-Step Solution

Answer

The required answer is $e^2{x}^{e^{2-1}}$.

Step 1. Given information.

The given function is:

$f\left(x\right)={\left(x^e\right)}^e$

Step 2. Find the derivative of the given function.

$$\begin{gathered} f\left(x\right)={\left(x^e\right)}^e \\ f\text{'}\left(x\right)=\frac{d}{dx}{\left(x^e\right)}^e \\ =\frac{d}{dx}{x}^{e^2} \\ =e^2{x}^{e^{2-1}} \end{gathered}$$