Chapter 12: Q. 31 (page 944)

Find the first-order partial derivatives for the functions in Exercises 27–36.
$f (x, y) = x \sin y$

Short Answer

Expert verified

The first-order partial derivatives are $\frac{\partial f}{\partial x} = \sin y and \frac{\partial f}{\partial y} = x \cos y .$

Step by step solution

Given

The given function is: $f (x, y) = x \sin y$

To find

We have to find the first-order partial derivatives.

Calculation

$f (x, y) = x \sin y \frac{\partial f}{\partial x} = \frac{\partial}{\partial x} (x \sin y) \frac{\partial f}{\partial x} = \sin y f (x, y) = x \sin y \frac{\partial f}{\partial y} = \frac{\partial}{\partial y} (x \sin y) \frac{\partial f}{\partial y} = x \frac{\partial}{\partial y} (\sin y) \frac{\partial f}{\partial y} = x \cos y Hence, \frac{\partial f}{\partial x} = \sin y and \frac{\partial f}{\partial y} = x \cos y .$

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Find the first-order partial derivatives for the functions in Exercises 27–36.
$f (x, y) = x \sin y$

Short Answer

Step by step solution

Given

To find

Calculation

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Find the first-order partial derivatives for the functions in Exercises 27–36. fx,y=xsiny

Short Answer

Step by step solution

Given

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Calculation

One App. One Place for Learning.

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Find the first-order partial derivatives for the functions in Exercises 27–36.
$f (x, y) = x \sin y$