Question: If U = tan^-1 (x^3 + y^3 / x -y) prove that x.du/dx + y du/dy = sin.2u

If U = tan^-1 (x^3 + y^3 / x -y) prove that

If U = tan^-1 (x^3 + y^3 / x -y) prove that x.du/dx + y du/dy = sin.2u

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

The detailed ... 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 Mathematics Questions!

Q:

Prove each of these identities. a. sin x/ tan x = cos x b. cos x sin x/ tan x = 1 sin 2 x c. 1 sin 2 x/cos x = cos x d. e. (sin x + cos x) 2 = 1 + 2 sin x cos x f. tan 2 x sin 2 x = tan 2 x sin 2...

Q:

Prove that u - v2 = u2 + v2 - 2u v.

Q:

Prove that if X and Y are two independent random variables, then U = g(X) and V = h(Y) are also independent.

Q:

Utility functions for auto and public transit between two towns are: UAUTO= -0.160 -0.011 (TT)-0.024. (C) -0.008 (WT) UPT = -0.224 -0.011 (TT) -0.024. (C) -0.013 (WT) Mode COST (C) Auto 20.5 PT 3.75...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

Question 1 Recall the formula for tan(a + b) in terms of tan(a) and tan(b): tan(a,) +tan(b) \"mm + b) = 1tan(a,) tan(b) ' Now use this to write tan1(m) + tan1 (y) = tan1(0) where 6 = E. What might be...

Q:

here are the questions. Thank you (a) Let f | D - R be a real valued function from R" to R with domain D in R", n > 2. Given a E D, define the directional derivative of f at a in the direction u,...

Q:

Instructions: Supply the correct answer, highlight your final answer, each question is numbered. 1.The Marginal Rate of Substitution & Utility Given the data below, find the MRS and complete the...

Q:

(1) Prove that if P(B) = 0 then B and A are independent for any event A. Prove the same if P(B) = 1. (2) Roll two fair die and let X1, X2 be their values. (a) Calculate P(X1 = 6|X1 + X2 = 10). (b)...

Q:

Second Derivatives 2 CW A. Find d2 or f\"(x) for the following functions. x [ml 1. f(x)=%x3%x2x+5 6) f(x) = ln(cos 5x) f'(x) = ( sin 5x)(5) cos 5x = _ sin 5x cos 5x @ Q) = 5 tan 5x f "(x) = 5 sec2 5x...

Q:

What are some of the product strategies and communication strategies that General Motors could use to further enhance the level of perceived differentiation between its divisions?

Q:

1. Compute the magnitude of the following complex numbers (a) 1+i (b) 1-i (c) (d) 3+14 1+i (e) 3em 2. Evaluate the quantity e for each of the given values of 0. Give your answer in rectangular form...

Q:

Find the flux o f the vector field out o f the closed box 0 x 2 , 0 y 3 , 0 z 4 . vec ( H ) = xyvec ( i ) + zvec ( j ) + yvec ( k ) Enter a n exact answer. Flux =

Q:

a) Roger Rogue owned an Electrical Products business. Roger sold his business to Roger Electrical Pty Ltd, which he incorporated because he was worried about a decrease in sales and an escalation of...

Q:

A woman worked part-time certain number of days, receiving for her pay $ 1800. If she had received $ 10 per day less than she did, she would have had to work 3 days longer to earn the same sum. How...

Q:

a. What is a prerefunded bond? b. Identify two reasons why an issuing municipality would want to prerefund an outstanding bond.

Q:

A variant of Clarke's Third Law is Any sufficiently crappy research is indistinguishable from fraud." A variant of Elizabeth Holmes "crappy research, lies, and chicanery kept Theranos, afloat for 15...

Q:

A treasure hunter walks along a straight shoreline at the rate of 3 miles per hour in search of buried treasure. A pirate ship is anchored 4 miles from the shore, directly across from their buried...

Q:

1. St. Anne Medical Center plans to use 300 million in 7 years to build a new Heart and Vascular Institute. As the hospital's finance manager, explain how the investment objective (future...

Q:

How many license plates can be made using either two or three uppercase English letters followed by either two or three digits?

Q:

Give a recursive algorithm for finding the reversal of a bit string. (See the definition of the reversal of a bit string in the preamble of Exercise 34 in Section 5.3.)

Q:

Construct a truth table for each of these compound propositions. a) p (q r) b) p (q r) c) (p q) (p r) d) (p q) (p r) e) (p q) (q r) f) (p q) (q r)

Q:

Using the data in file statepop.dat, draw a histogram, using the weights, of the number of veterans. Howdoes this compare with a histogram that does not use the weights? The file statepop.dat...

Q:

The Rao-Hartley-Cochran (1962) method for selecting psus with unequal probabilities. To take a sample of size n, divide the population into n random groups of psus, U1, U2, . . . ,Un. Then select one...

Q:

Suppose you want to take a sample of students in a university but your sampling frame is a list of all classes offered by the university. A student may be in more than one class, so a probability...