Question

Calculate. $$\frac{d}{d x}\left(\int_{1}^{x^{2}} \frac{d t}{t}\right)$$

Name: Problem 18, Chapter 5: Calculus: One Variable
Uploaded: 2021-08-21T06:07:33-08:00
Duration: 1 min 7 s
Channel: Adrian Co
Description: Calculate. (d)/(d x)(∫1^x^2 (d t)/(t))

   Calculate.
$$\frac{d}{d x}\left(\int_{1}^{x^{2}} \frac{d t}{t}\right)$$

Calculus: One Variable

Garret J. Etgen,… 10th Edition

Chapter 5, Problem 18

Instant Answer

Solved by Expert Adrian Co

08/21/2021

Step 1

According to the Fundamental Theorem of Calculus, the derivative of an integral of a function from a constant to a variable is simply the function evaluated at the variable. Show more…

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Calculate. $$\frac{d}{d x}\left(\int_{1}^{x^{2}} \frac{d t}{t}\right)$$

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Key Concepts

Fundamental Theorem of Calculus

This theorem establishes the connection between differentiation and integration, stating that if you differentiate an integral where the upper limit is a function of x, you recover the original integrand evaluated at that upper limit. It is essential for solving problems that involve the differentiation of an integral with variable limits.

Chain Rule

The chain rule is used when the function being differentiated is composed with another function. In the context of an integral with an upper limit expressed as a function of x, the chain rule is applied to account for the derivative of this inner function, ensuring that the overall derivative correctly reflects how changes in x affect the upper limit.

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