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Chapter 12: Q. 10 (page 988)

Describe the meanings of each of the following mathematical expressions:
$\frac{\partial w}{\partial z}$

Short Answer

Expert verified

Ans: $\frac{\partial w}{\partial z}$ It means a partial derivative of w with respect to z. Or the partial rate of change of w with respect to z.

Step by step solution

Step 1. Given information.

given, $\frac{\partial w}{\partial z}$

Step 2. The meaning of the given expression is,

$\frac{\partial w}{\partial z}$ It means a partial derivative of w with respect to z. Or the partial rate of change of w with respect to z.

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Most popular questions from this chapter

Use Theorem 12.33 to find the indicated derivatives in Exercises 27–30. Express your answers as functions of two variables.

$\frac{\partial z}{\partial t} w h e n z = x^{2} y^{3}, x = t \sin s, a n d y = s \cos t$

Describe the meanings of each of the following mathematical expressions :

$\frac{\partial w}{\partial y}$

Use Theorem 12.33 to find the indicated derivatives in Exercises 27–30. Express your answers as functions of two variables.

$\frac{\partial z}{\partial θ} w h e n z = (x^{2} + x y) e^{y}, x = r \cos θ a n d y = r \sin θ$

Solve the exact differential equations in Exercises 63–66. $y \cos (x y) - 3 + (x \cos (x y) + 2) \frac{d y}{d x} = 0 .$

Given a function of three variables, $w = f (x, y, z),$ and a constraint equation $g (x, y, z) = 0,$ how many equations would we obtain if we tried to optimize f by the method of Lagrange multipliers?

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Describe the meanings of each of the following mathematical expressions: ∂w∂z

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The meaning of the given expression is,

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Describe the meanings of each of the following mathematical expressions:
$\frac{\partial w}{\partial z}$