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Chapter 4: Q15P (page 191)

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

(鈭�z鈭�胃)r.

Short Answer

Expert verified

The value of provided equation is 鈭�z鈭�胃r=r2sin2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, 2 and 3,

z=(rcos胃)2+2rsin胃2z=r2(cos2胃+2sin2胃)

Take the partial derivative of with respect to '胃',

鈭�z鈭�胃=鈭�鈭�胃r2(1+sin2胃)=2r2sin胃cos胃

Now, differentiate partially with respect to 'r'

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