Answer
$f'(-2)$ is undefined.
Work Step by Step
Applying the chain rule with $u=x+2\to \dfrac{du}{dx}=1\to$
$f'(x)=\dfrac{2}{3\sqrt[3]{x+2}}; x\ne -2$
$f'(-2)$ is undefined.
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.