Q3P If z=Inu2+v2+w2,find聽鈭倆/鈭倁,... [FREE SOLUTION]

Chapter 4: Q3P (page 190)

If $z = I n \sqrt{u^{2} + v^{2} + w^{2}}$ ,find $鈭� z / 鈭� u, 鈭� z / 鈭� v, 鈭� z / w$

Short Answer

Expert verified

The value of provided equation is $\frac{鈭� z}{鈭� u} = \frac{u}{u^{2} + v^{2} + w^{2}} \frac{未 z}{未 v} = \frac{v}{u^{2} + v^{2} + w^{2}}$ , and $\frac{未 z}{未 w} = \frac{w}{u^{2} + v^{2} + w^{2}}$ .

Step by step solution

Explanation of solution

In this question, it is provided that $z = In \sqrt{u^{2} + v^{2} + w^{2}}$ and

Find $鈭� z / 鈭� u, 鈭� z / 鈭� v, 鈭� z / w$

Partial differentiation

The procedure of calculating the partial derivative of a function is called partial differentiation. This method is used to get the partial derivative of a function with respect to one variable while keeping the other constant.

Calculation

It is provided that $z = \sqrt{u^{2} + v^{2} + W^{2}}$

Implies that,

$z = \frac{1}{2} I n (u^{2} + v^{2} + w^{2})$

Now, Take partial derivative of z with respect to u,

$\frac{未 z}{未 u} = \frac{未}{未 u} [\frac{1}{2} I n (u^{2} + v^{2} + w^{2})] = \frac{1}{2} \frac{未}{未 u} I n (\frac{1}{u^{2} + v^{2} + w^{2}}) 脳 (2 u)$

So,

$\frac{鈭� z}{鈭� u} = \frac{u}{u^{2} + v^{2} + w^{2}}$

Now,

$\frac{未 z}{未 u} = \frac{未}{未 u} [\frac{1}{2} I n (u^{2} + v^{2} + w^{2})] = \frac{1}{2} . \frac{未}{未 u} . I n . (u^{2} + v^{2} + w^{2}) . 2 v = \frac{1}{2} (\frac{1}{u^{2} + v^{2} + w^{2}}) . 2 v$

So,

$\frac{未 z}{未 v} = \frac{v}{u^{2} + v^{2} + w^{2}} Similarly, \frac{未锄}{未飞} = \frac{w}{u^{2} + v^{2} + w^{2}}$

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If $z = I n \sqrt{u^{2} + v^{2} + w^{2}}$ ,find $鈭� z / 鈭� u, 鈭� z / 鈭� v, 鈭� z / w$

Short Answer

Step by step solution

Explanation of solution

Partial differentiation

Calculation

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91影视

If z=Inu2+v2+w2,find鈭�z/鈭�u,鈭�z/鈭�v,鈭�z/w

Short Answer

Step by step solution

Explanation of solution

Partial differentiation

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Electrostatics

Work Energy and Power

Force

Solid State Physics

Measurements

Study anywhere. Anytime. Across all devices.

If $z = I n \sqrt{u^{2} + v^{2} + w^{2}}$ ,find $鈭� z / 鈭� u, 鈭� z / 鈭� v, 鈭� z / w$