What's the derivative of the following function?
Answer
Most of these (although not all) will be straightforward applications of the quotient rule.
We could rewrite this as if we wanted.
What is f ' (x) for the following function?
We could also rewrite this as
What's the derivative of the function?
There isn't any better way to write this one.
What is the derivative of f with respect to x?
We wouldn't bother rewriting this. Don't even multiply out the bottom—it's not worth it.
the derivative is
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.
Find the derivative of the following function.
Hint
Rewrite the function first.
Now we can use the quotient rule, remembering that ln 5 is a constant:
What is the derivative of the following function.
This is as simplified as the answer gets. Yuck!
rewrite first
Now taking the derivative is possible:
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if we wanted.
