Chapter 4: Q10MP (page 239)

If $w = {(r c o s 胃)}^{r s i n 胃}$ , find $\frac{鈭� w}{鈭� 胃}$ .

Short Answer

Expert verified

The value of $\frac{鈭� w}{鈭� 胃} is [x In x - \frac{y^{2}}{x}] x^{y}$ .

Step by step solution

Given Information

Given that, $w = {(r \cos 胃)}^{r \sin 胃}$ .

Concept

To find out the value of $\frac{鈭� w}{鈭� 胃}$ take logarithm on both the sides.

Finding the value of ∂w∂θ

Take logarithm on both the sides

$\log w = \log ({(r \cos 胃)}^{(r \sin 胃)})$

This can also be written as $\log w = (r \sin 胃) \log (r \cos 胃)$

Now differentiating the above function with respect to

$\frac{1}{w} \frac{鈭� w}{鈭� 胃} = (r \sin 胃) \frac{- r \sin 胃}{r \cos 胃} + \log (r \cos 胃) r \cos 胃 \frac{鈭� w}{鈭� 胃} = [\log (r \cos 胃) . r \cos 胃 - \frac{r^{2} \sin^{2} 胃}{r \cos 胃}] {(r \cos 胃)}^{(r \sin 胃)} \frac{鈭� w}{鈭� 胃} = [x In x - \frac{y^{2}}{x}] x^{y}$

Where, $x = r \cos 胃, y = r \sin 胃$ .

Hence $\frac{鈭� w}{鈭� 胃} = [x In x - \frac{y^{2}}{x}] x^{y}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

If $w = {(r c o s 胃)}^{r s i n 胃}$ , find $\frac{鈭� w}{鈭� 胃}$ .

Short Answer

Step by step solution

Given Information

Concept

Finding the value of ∂w∂θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Medical Physics

Fundamentals of Physics

Space Physics

Fluids

Dynamics

Study anywhere. Anytime. Across all devices.

91影视

Ifw=(rcos胃)rsin胃, find鈭�w鈭�胃.

Short Answer

Step by step solution

Given Information

Concept

Finding the value of ∂w∂θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Medical Physics

Fundamentals of Physics

Space Physics

Fluids

Dynamics

Study anywhere. Anytime. Across all devices.

If $w = {(r c o s 胃)}^{r s i n 胃}$ , find $\frac{鈭� w}{鈭� 胃}$ .