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Chapter 4: Q10P (page 191)

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

(鈭�z鈭�y)x.

Short Answer

Expert verified

The value of provided equation is鈭�z鈭�yx=4y .

Step by step solution

01

Given data

The given data are listed below

z=x2+2y2.....1x=rcos胃.....2y=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

 Step 3: Calculation

Consider that,

z=x2+2y2

Take the partial derivative of with respect to y ,

鈭�z鈭�yx=鈭�鈭�yx2+2y2=鈭�鈭�yx2+鈭�鈭�y2y2鈭�z鈭�yx=0+4y

Therefore,

鈭�z鈭�yx=0+4y

Therefore,

鈭�z鈭�yx=4y

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