Question: Let (x, y) = x 2 + y 2 and r(t) = (cos t, sin t). (a) Find d/dt(r(t)) without making any calculations. Explain. (b)

Let ƒ(x, y) = x2 + y2 and r(t) = (cos t, sin t).

(a) Find d/dtƒ(r(t)) without making any calculations. Explain.
(b) Verify your answer to (a) using the Chain Rule.

Step by Step Solution

★★★★★

3.43 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a The level curves of fx y are the circles y r Since ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Q:

A string is wound around a uniform disk of radius R and mass M. The disk is released from rest with the string vertical and its top end tied to a fixed bar (Fig. P10.77). Show that (a) The tension in...

Q:

Complete the function compute using pthreads v1() to parallelize the SAXPY loop using the "chunking" method. That is, given vectors x and y of some arbitrary length n, and when k threads are used,...

Q:

Find the polar equation for the curve described by the following Cartesian equations. a. y = 45 b. x2 + y2 = 36 c. x2 - y2 = 1 d. 4xy = 1 e. y = 3x + 2 f. 3x2 + 4y = 2 g. x2 + 2x + y2 - 4y - 25 = 0...

Q:

Find the general solution of the differential equation zy/ + 2y/ - (x + 2) cos (x) + y =0 and choose the correct answer from the following options. O 1 y = 2 (I (Isin (x) + 2 sin (x) + cos (x)) + C)...

Q:

Can you please help me with number 12 and number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.6 Problems Find...

Q:

Exercise 1: Read both the introduction to the section and Example 1 (p. 969 - 971). Explain what the differential ds is substituted with in the computation of the line integral here. The subsection...

Q:

for part 5 chose one a or b 1. The following matrices are related. A' is row-equivalent to A, and A" is the transpose of A. Use this information to complete the following: N 2 1 -6 00 Co its co 3 A =...

Q:

Two statements are given below. For each, an erroneous proof is provided. There is one main error in each proof. State what this error is and explain why it is an error. (Note that the rst of these...

Q:

PLEASE ANSWER ALL CORRECT AND SHOW ALL WORK I GIVE AMAZING REVIEWS A curve is described by the following parametric equations: x=3+ y= t2-4 Which statement best describes the curve? (1 point) O The...

Q:

1. [-/0.273 Points] DETAILS LARCALC11 12.2.004. Find r'(2), r(t,), and r\\to) for the given value of to- r(t) = (5 + gi + #j, to = 1 r(0) = r(t ) r '(t ) Sketch the curve represented by the...

Q:

An investigation is conducted to determine if the mean age of welfare recipients differs between two cities A and B. Random samples of 75 and 100 welfare recipients are selected from city A and city...

Q:

You are considering buying a particular stock. You expect to own the stock for the next four years. The stock's current market price is $24.50, and you expect to sell it for $55 in four years. You...

Q:

This is all one problem please do the math and plotting. Use matlab for this, i need help.

Q:

=+3 Discuss the financial factors, other than the cost of the plan, and the non-financial factors that should be considered in selecting an appropriate payment plan.

Q:

Identify and graph the polar equation. r = 4 + 2sin

Q:

Identify and graph the polar equation. r = 1 + 2sin

Q:

Identify and graph the polar equation. r = 1 - 2sin

Q:

In terms of network security, what should organizational management allow and what should they block? Network Security book (see pages. 248-251)

Q:

Refer to the figure above. The Degree of Financial Leverage is 1.29x 4.50x 3.50x 1.32x

Q:

what are the tools the network administrator would use for managing a network, describe at least two tools used for network administration that can be used for a forensic investigation. How would...