Chapter 4: Q2P (page 201)

Given $w = \sqrt{u^{2} + v^{2}}$ ,
$u = \cos [Intan (p + \frac{1}{4} π)] v = \sin [In \tan (p + \frac{1}{4} π)]$ , find $\frac{d w}{d p}$ .

Short Answer

Expert verified

The value of $\frac{d w}{d p}$ is zero.

Step by step solution

Explanation of solution

The provided expressions are $w = \sqrt{u^{2} + v^{2}}$ ,

$u = \cos [Intan (p + \frac{1}{4} π)] v = \sin [In \tan (p + \frac{1}{4} π)]$

Chain Rule

The number of functions in the composition affects how many differentiation steps are required when using the chain rule to get the derivative of composite functions.

Calculation

Use the below equation.

$d w = \frac{\partial w}{\partial u} d u + \frac{\partial w}{\partial v} d v$

Therefore, the value of in term ofp is,

$w = \sqrt{[\cos {[In \tan (p + \frac{1}{4} π)]}^{2} + \sin {[In \tan (p + \frac{1}{4} π)]}^{2}]} = \sqrt{[\cos {[In \tan (p + \frac{1}{4} π)]}^{2} + \sin^{2} [In \tan (p + \frac{1}{4} π)]]}$

Use identity $\sin^{2} x + \cos^{2} x = 1$ in above equation.

$w = \sqrt{1} = 1$

Thus, w is a constant function, and that the derivative of a constant function is always zero.

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Given $w = \sqrt{u^{2} + v^{2}}$ ,
$u = \cos [Intan (p + \frac{1}{4} π)] v = \sin [In \tan (p + \frac{1}{4} π)]$ , find $\frac{d w}{d p}$ .

Short Answer

Step by step solution

Explanation of solution

Chain Rule

Calculation

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Givenw=u2+v2,u=cos[Intanp+14π]v=sin[Intanp+14π], finddwdp.

Short Answer

Step by step solution

Explanation of solution

Chain Rule

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Given $w = \sqrt{u^{2} + v^{2}}$ ,
$u = \cos [Intan (p + \frac{1}{4} π)] v = \sin [In \tan (p + \frac{1}{4} π)]$ , find $\frac{d w}{d p}$ .