Combination of Product Rule and Chain Rule Problems

by Beth Flarrity

How do we find the derivative of the following functions?

Answer by Pablo:

In these two problems posted by Beth, we need to apply not only the chain rule, but also the product rule. If you still don't know about the product
rule, go inform yourself here: the product rule.

Now, for the first of these we need to apply the product rule first:

To find the derivative inside the parenthesis we need to apply the chain rule. We already know how to derive functions inside square roots:

Now, for the second problem we may rewrite the expression of the function first:

Now we can apply the product rule:

And that's the answer.

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