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Chapter 4: Q14P (page 191)

Ifz=x2+2y2,x=rcos胃,y=rsin胃find the following partial derivatives.

(鈭�z鈭�胃)y.

Short Answer

Expert verified

The value of provide equation is 鈭�z鈭�胃y=-2r2sin2胃.

Step by step solution

01

Given data

The given data are listed below

z=x2+2y2 ...(1)

x=rcos胃 ...(2)

y=rsin胃 ...(3)

02

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,

z=(rcos胃)2+2y2z=r2cos2胃+2y2

Take the partial derivative of 'z' with respect to '胃' in above equation;

role="math" localid="1659092547223" 鈭�z鈭�胃y=鈭�鈭�胃r2cos2胃+2y2=2r2sin胃路cos胃鈭�z鈭�胃y=2r2sin2胃

Hence,

鈭�z鈭�胃y=2r2sin2胃

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