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Chapter 4: Q18P (page 191)

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

(鈭�z鈭�r)y

Short Answer

Expert verified

The value of provided equation is 鈭�z鈭�ry=2r.

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

Square the equation 2 and 3, then add.

x2+y2=r2 ...(4)

From equation (1),

z=r2+y2z=x2+y2+y2z=x2+2y2

Take the partial derivative of z with respect to ,

鈭�z鈭�ry=鈭�鈭�rr2+y2鈭�z鈭�ry=2r

Hence,鈭�z鈭�ry=2r

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