Question
Find the derivative and simplify your
answer.
answer.
Ask by Mullins Floyd. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The derivative is
.
Solution
We begin with the integral
Since the upper limit is a function of
, we use the Fundamental Theorem of Calculus together with the chain rule (Leibniz rule). If
then
In our case, we have:
-
. -
with .
Thus, substituting in, we get:
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Bonus Knowledge
To find the derivative, we can use the Fundamental Theorem of Calculus, which tells us that:
In your case,
and
.
First, we need to compute
:
Next, we differentiate
:
Now we can apply the theorem:
Thus, the derivative simplifies to:
So the final answer you are looking for is:
And, filling in the placeholders: