/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q9P if z=x2+2y2聽,聽x=r聽cos胃,y=sin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q9P (page 191)

if z=x2+2y2,x=rcos胃,y=sin胃, find the following partial derivatives.

(鈭�z鈭�x)胃.

Short Answer

Expert verified

The value of provided equation is (鈭�z鈭�x)胃=2x1+2tan2胃.

Step by step solution

01

Given data

The given data are listed below

z=x2+2y2....1x=rcos胃....2y=rsin胃......3

02

 Step 2: Partial differentiation

The procedure of calculating the partial derivative of a function is called partial differentiation. This method is used to get the partial derivative of a function with respect to one variable while keeping the other constant.

03

Calculation

From equation 1 and 2,

yx=tan胃y=xtan胃

Substitute the value of y in equation 1.

z=x2+2xtan胃2z=x21+2tan2胃

Take the partial derivative of zwith respect to x,

role="math" localid="1659009652553" 鈭�z鈭�x胃=鈭�鈭�xx21+2tan2胃鈭�z鈭�x胃=2x1+2tan2胃

Therefore,鈭�z鈭�x胃=2x1+2tan2胃.

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

Most popular questions from this chapter

Ifyexy=sinx finddy/dx andd2y/dx2 atrole="math" localid="1658830042567" (0,0) .

Find the two-variable Maclaurin series for the following functions.

cos x sinh y

Given particles of masses m, 2m, and 3m at the points(0,1),(1,0), and (2,3), find the point P about which their total moment of inertia will be least. (Recall that to find the moment of inertia of m about P, you multiply m by the square of its distance from P.

Find by the Lagrange multiplier method the largest value of the product of three positive numbers if their sum is 1.

What proportions will maximize the volume of a projectile in the form of a circular cylinder with one conical end and one flat end, if the surface area is given?
See all solutions

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Medical Physics

Read Explanation

Classical Mechanics

Read Explanation

Wave Optics

Read Explanation

Waves Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.