* Part 4: A derivative computation using the FTC and the chain rule d d (F(x*) dx dt dx

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Part 4: A Derivative Computation Using the FTC and the Chain Rule

\[
\frac{d}{dx} \left( F(x^4) \right) = \frac{d}{dx} \left( \int_{13}^{x^4} e^{-t^2} \, dt \right)
\]

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Explanation: There is a mathematical formula and integral expression involving derivatives, the Fundamental Theorem of Calculus (FTC), and the chain rule. Students are instructed to compute the derivative with respect to \( x \) of the given integral function.

Please ensure you understand both the FTC and chain rule principles to successfully solve this type of problem. This problem is designed to test your knowledge in combining these calculus concepts.

Remember, even if your answer isn't entirely correct, you can still receive partial credit based on your attempt. Use the provided buttons to review your answers or submit them for grading.
Transcribed Image Text:### Part 4: A Derivative Computation Using the FTC and the Chain Rule \[ \frac{d}{dx} \left( F(x^4) \right) = \frac{d}{dx} \left( \int_{13}^{x^4} e^{-t^2} \, dt \right) \] --- **Note:** You can earn partial credit on this problem. --- - **Preview My Answers** (button) - **Submit Answers** (button) --- You have attempted this problem 23 times. Your overall recorded score is 83%. --- Explanation: There is a mathematical formula and integral expression involving derivatives, the Fundamental Theorem of Calculus (FTC), and the chain rule. Students are instructed to compute the derivative with respect to \( x \) of the given integral function. Please ensure you understand both the FTC and chain rule principles to successfully solve this type of problem. This problem is designed to test your knowledge in combining these calculus concepts. Remember, even if your answer isn't entirely correct, you can still receive partial credit based on your attempt. Use the provided buttons to review your answers or submit them for grading.
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