Q. 27 Find the first-order partial der... [FREE SOLUTION]

Chapter 12: Q. 27 (page 944)

Find the first-order partial derivatives for the functions in Exercises 27鈥�36.
$f (x, y) = e^{x} \sin (x y)$

Short Answer

Expert verified

The first order partial derivatives are $f_{x} (x, y) = e^{x} \sin (x y) + y e^{x} \cos (x y) and f_{y} (x, y) = x e^{x} \cos (x y)$

Step by step solution

Given

The given function is: $f (x, y) = e^{x} \sin (x y)$ .

To find

We have to find the first-order partial derivatives.

Calculation

$f (x, y) = e^{x} \sin (x y) f_{x} (x, y) = \frac{鈭�}{鈭� x} (e^{x} \sin (x y)) f_{x} (x, y) = \frac{鈭�}{鈭� x} (e^{x}) \sin (x y) + e^{x} \frac{鈭�}{鈭� x} (\sin (x y)) f_{x} (x, y) = e^{x} \sin (x y) + e^{x} \cos (x y) \frac{鈭�}{鈭� x} (x y) f_{x} (x, y) = e^{x} \sin (x y) + e^{x} \cos (x y) (y) f_{x} (x, y) = e^{x} \sin (x y) + y e^{x} \cos (x y) f (x, y) = e^{x} \sin (x y) f_{y} (x, y) = \frac{鈭�}{鈭� y} (e^{x} \sin (x y)) f_{y} (x, y) = \frac{鈭�}{鈭� y} (e^{x}) \sin (x y) + e^{x} \frac{鈭�}{鈭� y} (\sin (x y)) f_{y} (x, y) = (0) \sin (x y) + e^{x} (\cos (x y)) \frac{鈭�}{鈭� y} (x y) f_{y} (x, y) = 0 + e^{x} \cos (x y) (x) f_{y} (x, y) = x e^{x} \cos (x y) Hence, f_{x} (x, y) = e^{x} \sin (x y) + y e^{x} \cos (x y) and f_{y} (x, y) = x e^{x} \cos (x y)$

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91影视

Find the first-order partial derivatives for the functions in Exercises 27鈥�36.
$f (x, y) = e^{x} \sin (x y)$

Short Answer

Step by step solution

Given

To find

Calculation

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91影视

Find the first-order partial derivatives for the functions in Exercises 27鈥�36.fx,y=exsinxy

Short Answer

Step by step solution

Given

To find

Calculation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Find the first-order partial derivatives for the functions in Exercises 27鈥�36.
$f (x, y) = e^{x} \sin (x y)$