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Chapter 12: Q. 3 (page 988)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

given,

$\frac{\partial w}{\partial x}$

Step 2. The meaning of the given expression is,

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

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Most popular questions from this chapter

Evaluate the following limits, or explain why the limit does not exist.

$\lim_{(x, y) \to (0, 0)} \frac{x + y}{x^{2} + y^{2}}$

In Exercises, find the maximum and minimum of the function f subject to the given constraint. In each case explain why the maximum and minimum must both exist.

$f (x, y) = x y when x^{2} + y^{2} = 16$

Find the directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.

$f (x, y) = \frac{x + y}{x^{2} + y^{2}}, P = (1, 2), v = ⟨ 3, - 2 ⟩$

Use Theorem 12.32 to find the indicated derivatives in Exercises 21–26. Express your answers as functions of a single variable.

$\frac{d y}{d t} w h e n y = r \sin θ, r = t^{3}, a n d θ = \sqrt{t}$

Find the directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.

$f (x, y, z) = \sqrt{\frac{x y}{z}}, P = (2, 3, 1), v = ⟨ 2, 1, - 2 ⟩$

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Describe the meanings of each of the following mathematical expressions ∂w∂x

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
$\frac{\partial w}{\partial x}$