Q12-10P Find聽dydx explicitly if y=鈭�01... [FREE SOLUTION]

91影视

Chapter 1: Q12-10P (page 1)

Find $\frac{d y}{d x}$ explicitly if $y = {鈭�}_{0}^{1} \frac{e^{x u} - 1}{u} d u$ .

Short Answer

Expert verified

The value of $\frac{d y}{d x}$ is $\frac{e^{x} - 1}{x}$ .

Step by step solution

Given Information

Given that $y = {鈭�}_{0}^{1} \frac{e^{xu} - 1}{u} d u$ . ...(1)

Formula Used

We know that $\frac{d}{d x} {鈭�}_{u (x)}^{v (x)} f (x, t) d t = f (x, v) \frac{d v}{d x} - f (x, u) \frac{d u}{d x} + {鈭�}_{u}^{v} \frac{鈭� f}{鈭� x} d t$ ...(2)

Finding the value of dydx

Compare equation (1) and equation (2).

$\frac{d}{d x} (y) = \frac{d}{d x} {鈭�}_{0}^{1} \frac{e^{x u} - 1}{u} d u \frac{d y}{d x} = \frac{e^{x (1)} - 1}{1} 路 \frac{d}{d x} (1) - \frac{e^{x (0)} - 1}{1} 路 \frac{d}{d x} (0) + {鈭�}_{0}^{1} u \frac{e^{x u}}{u} d u \frac{d y}{d x} = \frac{e^{x (1)} - 1}{1} (0) - \frac{e^{x (0)} - 1}{1} (0) + {鈭�}_{0}^{1} e^{x u} d u \frac{d y}{d x} = {鈭�}_{0}^{1} e^{x u} d u$

Solving further,

$\frac{d y}{d x} = {[\frac{e^{x u}}{x}]}_{0}^{1} = \frac{1}{x} (e^{x (1)} - e^{x (0)}) = \frac{e^{x} - 1}{x}$

Therefore, $\frac{d y}{d x} = \frac{e^{x} - 1}{x}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Find $\frac{d y}{d x}$ explicitly if $y = {鈭�}_{0}^{1} \frac{e^{x u} - 1}{u} d u$ .

Short Answer

Step by step solution

Given Information

Formula Used

Finding the value of dydx

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Physics of Motion

Circular Motion and Gravitation

Magnetism

Turning Points in Physics

Space Physics

Study anywhere. Anytime. Across all devices.

91影视

Finddydx explicitly if y=鈭�01exu-1udu.

Short Answer

Step by step solution

Given Information

Formula Used

Finding the value of dydx

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Physics of Motion

Circular Motion and Gravitation

Magnetism

Turning Points in Physics

Space Physics

Study anywhere. Anytime. Across all devices.

Find $\frac{d y}{d x}$ explicitly if $y = {鈭�}_{0}^{1} \frac{e^{x u} - 1}{u} d u$ .