Q 70. Prove that鈭�(f(x,y)g(x,y))=f(x,... [FREE SOLUTION]

Chapter 12: Q 70. (page 965)

Prove that
$鈭� (f (x, y) g (x, y)) = f (x, y) 鈭� g (x, y) + g (x, y) 鈭� f (x, y)$

Short Answer

Expert verified

Solve $鈭� (伪 f (x, y) + 尾 g (x, y)) = i \frac{鈭� (伪 f (x, y) + 尾 g (x, y))}{鈭� x} + j \frac{鈭� (伪 f (x, y) + 尾 g (x, y))}{鈭� y}$ for proving above relation.

Step by step solution

Given Information

Considering function

$f (x, y), g (x, y)$

We need to show that

$鈭� (伪 f (x, y) + 尾 g (x, y)) = 伪鈭� f (x, y) + 尾鈭� g (x, y)$

Simplification

Solving for $鈭� (伪 f (x, y) + 尾 g (x, y)) = i \frac{鈭� (伪 f (x, y) + 尾 g (x, y))}{鈭� x} + j \frac{鈭� (伪 f (x, y) + 尾 g (x, y))}{鈭� y}$

$鈭� (伪 f (x, y) + 尾 g (x, y)) = i [\frac{伪鈭� (f (x, y)) + 尾鈭� (g (x, y))}{鈭� x}] + j [\frac{伪鈭� (f (x, y)) + 尾鈭� (g (x, y))}{鈭� y}]$

$鈭� (f (x, y) + g (x, y)) = [伪 i \frac{鈭� (f (x, y))}{鈭� x} + 伪 j \frac{鈭� (f (x, y))}{鈭� y}] + [尾 i \frac{鈭� (g (x, y))}{鈭� x} + 尾 j \frac{鈭� (g (x, y))}{鈭� y}]$

$鈭� (伪 f (x, y) + 尾 g (x, y)) = 伪鈭� f (x, y) + 尾鈭� g (x, y)$

Hence proved.

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Prove that
$鈭� (f (x, y) g (x, y)) = f (x, y) 鈭� g (x, y) + g (x, y) 鈭� f (x, y)$

Short Answer

Step by step solution

Given Information

Simplification

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91影视

Prove that鈭�(f(x,y)g(x,y))=f(x,y)鈭�g(x,y)+g(x,y)鈭�f(x,y)

Short Answer

Step by step solution

Given Information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Pure Maths

Decision Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Prove that
$鈭� (f (x, y) g (x, y)) = f (x, y) 鈭� g (x, y) + g (x, y) 鈭� f (x, y)$