Q. 54. For the partial derivatives give... [FREE SOLUTION]

Chapter 12: Q. 54. (page 944)

For the partial derivatives given in Exercises 51鈥�54, find the
most general form for a function of two variables, , with
the given partial derivative
$\frac{{鈭�}^{2} f}{鈭� y 鈭� x} = 0$

Short Answer

Expert verified

The required most general form of $f (x, y)$ so that $\frac{{鈭�}^{2} f}{鈭� y 鈭� x} = 0$ is $f (x, y) = h_{1} (x) + h_{2} (y)$

Step by step solution

Given information

Given derivative is $\frac{{鈭�}^{2} f}{鈭� y 鈭� x} = 0$

The objective is to find the most general form of a function f(x, y)

The most general form of a function $f (x, y)$ so that $\frac{{鈭�}^{2} f}{鈭� y 鈭� x} = 0$

Suppose, $f (x, y) = h_{1} (x) + h_{2} (y)$

Then,

$\frac{d f}{d x} = {h^{'}}_{1} (x) \frac{d^{2} f}{d y d x} = 0$

Hence, the most general form of $f (x, y)$ so that $\frac{{鈭�}^{2} f}{鈭� y 鈭� x} = 0$ is $f (x, y) = h_{1} (x) + h_{2} (y)$

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91影视

For the partial derivatives given in Exercises 51鈥�54, find the
most general form for a function of two variables, , with
the given partial derivative
$\frac{{鈭�}^{2} f}{鈭� y 鈭� x} = 0$

Short Answer

Step by step solution

Given information

The objective is to find the most general form of a function f(x, y)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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91影视

For the partial derivatives given in Exercises 51鈥�54, find themost general form for a function of two variables, , withthe given partial derivative鈭�2f鈭�y鈭�x=0

Short Answer

Step by step solution

Given information

The objective is to find the most general form of a function f(x, y)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Calculus

Logic and Functions

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

For the partial derivatives given in Exercises 51鈥�54, find the
most general form for a function of two variables, , with
the given partial derivative
$\frac{{鈭�}^{2} f}{鈭� y 鈭� x} = 0$