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Chapter 4: Q9P (page 191)

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

(鈭�z鈭�x)胃.

Short Answer

Expert verified

The value of provided equation is (鈭�z鈭�x)胃=2x1+2tan2胃.

Step by step solution

01

Given data

The given data are listed below

z=x2+2y2....1x=rcos胃....2y=rsin胃......3

02

 Step 2: 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 2,

yx=tan胃y=xtan胃

Substitute the value of y in equation 1.

z=x2+2xtan胃2z=x21+2tan2胃

Take the partial derivative of zwith respect to x,

role="math" localid="1659009652553" 鈭�z鈭�x胃=鈭�鈭�xx21+2tan2胃鈭�z鈭�x胃=2x1+2tan2胃

Therefore,鈭�z鈭�x胃=2x1+2tan2胃.

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