Chapter 4: Q7P (page 191)

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

Short Answer

Expert verified

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

Step by step solution

Explanation of solution

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

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 ,

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

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

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

Short Answer

Step by step solution

Explanation of solution

Partial differentiation

Calculation

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ifz=x2+2y2,x=rcosθ,y=sinθfind the following partial derivatives.(∂z∂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

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