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Chapter 4: Q11P (page 191)

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

(鈭�z鈭�y)r=2y.

Short Answer

Expert verified

Hence the value of provide equation is鈭�z鈭�yr=2y

Step by step solution

01

Explanation of solutionStep 1: 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, and then add.

x2+y2=r2 ...(4)

From equation (1),

z=(x2+y2)+y2z=r2+y2

Take the partial derivative of z with respect to y,

鈭�z鈭�yr=鈭�鈭�y(r2+y2)=2y

Hence,

鈭�z鈭�yr=2y

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