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Chapter 4: Q13P (page 191)

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

(鈭�z鈭�胃)x

Short Answer

Expert verified

The value of provide equation is 鈭�z鈭�胃x=4r2sin胃cos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 3,

z=x2+2(rsin胃)2z=x2+2r2sin2胃

Now, take the partial derivative with respect to in above equation,

role="math" localid="1659091215113" 鈭�z鈭�胃x=鈭�鈭�胃x2+2r2sin2胃鈭�z鈭�胃x=4r2sin胃cos胃

Hence,鈭�z鈭�胃x=4r2sin胃cos胃

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