Question
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Find the derivative and simplify your
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:

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

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:

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