Computing Derivatives Exercises

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Most of these (although not all) will be straightforward applications of the quotient rule.

We could rewrite this as if we wanted.

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We could also rewrite this as 

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There isn't any better way to write this one.

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We wouldn't bother rewriting this. Don't even multiply out the bottom—it's not worth it.

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• The denominator of this function is a constant, so we don't need to use the quotient rule. Since

the derivative is

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We recommend leaving the answer like this. Since we can see at a glance that the root of (x + 1)² is x = -1, this is a more useful expression than

x² + 2x + 1.

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• The first thing we do is rewrite the function:

Now we can use the quotient rule, remembering that ln 5 is a constant:

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This is as simplified as the answer gets. Yuck!

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• First we rewrite the function:

Now taking the derivative is possible: