Chapter 4: Q7P (page 191)

if $z = x^{2} + 2 y^{2}, x = r c o s 胃, y = s i n 胃$ find the following partial derivatives.
${(\frac{鈭� z}{鈭� x})}_{y}$ .

Short Answer

Expert verified

The value of provided equation is ${(\frac{鈭� z}{鈭� x})}_{y} = 2 x$ .

Step by step solution

Explanation of solution

In this question it is provided that $z = x^{2} + 2 y^{2}; x = r \cos 胃, y = r \sin 胃$ and to find ${(\frac{鈭� z}{鈭� x})}_{y}$ .

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.

Calculation

Consider that,

$z = x^{2} + 2 y^{2}$

Taking the partial derivative of z with respect to x ,

${(\frac{鈭� z}{鈭� x})}_{y} = \frac{鈭�}{鈭� x} = {(x^{2} + 2 y^{2})}_{y} {(\frac{鈭� z}{鈭� x})}_{y} = 2 x$

Hence the value of provided equation is ${(\frac{鈭� z}{鈭� x})}_{y} = 2 x$ .

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91影视

if $z = x^{2} + 2 y^{2}, x = r c o s 胃, y = s i n 胃$ find the following partial derivatives.
${(\frac{鈭� z}{鈭� x})}_{y}$ .

Short Answer

Step by step solution

Explanation of solution

Partial differentiation

Calculation

One App. One Place for Learning.

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91影视

ifz=x2+2y2,x=rcos胃,y=sin胃find the following partial derivatives.(鈭�z鈭�x)y.

Short Answer

Step by step solution

Explanation of solution

Partial differentiation

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Modern Physics

Translational Dynamics

Classical Mechanics

Space Physics

Kinematics Physics

Study anywhere. Anytime. Across all devices.

if $z = x^{2} + 2 y^{2}, x = r c o s 胃, y = s i n 胃$ find the following partial derivatives.
${(\frac{鈭� z}{鈭� x})}_{y}$ .