Q27. - Calculus

Question

Find the derivatives of the functions: $f\left(x\right) = e^{\left(e^x\right) }$

Step-by-Step Solution

Answer

The required answer is $e^{\left(e^x\right)}{e}^x$.

Step 1. Given information.

The given function is: $e^{\left(e^x\right)}$

Step 2. Find the derivative of the given function.

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