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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Use the Chain Rule to find dz/dt or dw/dt.

4. z = 1 + x y , x = tan t, y = arctan t

To determine

To find: The value of dzdt using Chain Rule if z=1+xy , x=tant and y=arctant .

Explanation

Chain Rule:

“Suppose that z=f(x,y) is a differentiable function of x and y , where x=g(t)andy=h(t) are both differentiable functions of t . Then, z is differentiable function of t and dzdt=zxdxdt+zydydt ”.

Calculation:

The functions z=1+xy . (1)

Take partial derivative with respect to x in the equation (1),

zx=121+xy(y)=y21+xy

Thus, the partial derivative, zx=y21+xy .

Take partial derivative with respect to y in the equation (1),

zx=121+xy(x)=x21+xy

Thus, the partial derivate, zy=x21+xy .

Obtain the partial derivative of x with respect to t .

x=tantdxdt=sec2t=sec2t

Thus, the derivate, dxdt=sec2t

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Chapter 14 Solutions

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P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-58RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8P

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