Answer
$$f^{(n)}(x) = 2^x(\ln 2)^n$$
Work Step by Step
Given $f(x)= 2^x$
Then
\begin{align*}
f'(x)&= 2^x\ln 2\\
f''(x)&= 2^x(\ln 2)^2\\
f'''(x)&= 2^x(\ln 2)^3\\
\vdots\ \ \ &=\vdots\\
f^{(n)}(x)&= 2^x(\ln 2)^n\\
\end{align*}
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.