Chapter 12: Q. 37 (page 961)

Find the gradient of the given functions in Exercises 37–42.
$z = x^{2} \sin y + y \sin x$

Short Answer

Expert verified

The gradient of the given function is $(2 x \sin y + y \cos x, x^{2} \cos y + \sin x)$ .

Step by step solution

Step 1. Given Information.

The given function is:

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

Step 2. Calculation.

The gradient of the given function is:

$z = f (x, y) = x^{2} \sin y + y \sin x \nabla f (x, y) = [f_{x} (x, y), f_{y} (x, y)] - - - - - - - (1)$

Now find

$f_{x} (x, y) = 2 x \sin y + y \cos x f_{y} (x, y) = x^{2} \cos y + \sin x$

Use these above values in (1) we get,

localid="1650186054791" $\nabla f (x, y) = (2 x \sin y + y \cos x, x^{2} \cos y + \sin x)$

Step 3. Conclusion.

The gradient of the given function is $(2 x \sin y + y \cos x, x^{2} \cos y + \sin x)$ .

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Find the gradient of the given functions in Exercises 37–42.
$z = x^{2} \sin y + y \sin x$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find the gradient of the given functions in Exercises 37–42.z=x2siny+ysinx

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the gradient of the given functions in Exercises 37–42.
$z = x^{2} \sin y + y \sin x$