1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
expeople1 [14]
3 years ago
12

Use chain rule to find dw/dt w=ln(x^2 + y^2 + z^2)^(1/2) , x=sint, y=cost, z=tant

Mathematics
1 answer:
son4ous [18]3 years ago
4 0
The chain rule states that

\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}

Since \ln(x^2+y^2+z^2)^{1/2}=\dfrac12\ln(x^2+y^2+z^2), you have

\dfrac{\partial w}{\partial x}=\dfrac x{x^2+y^2+z^2}
\dfrac{\partial w}{\partial x}=\dfrac y{x^2+y^2+z^2}
\dfrac{\partial w}{\partial z}=\dfrac z{x^2+y^2+z^2}

and

\dfrac{\mathrm dx}{\mathrm dt}=\cos t
\dfrac{\mathrm dy}{\mathrm dt}=-\sin t
\dfrac{\mathrm dz}{\mathrm dt}=\sec^2t

Also, since x^2+y^2+z^2=\sin^2t+\cos^2t+\tan^2t=1+\tan^2t=\sec^2t, the derivative is

\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\sin t\cos t}{\sec^2t}-\dfrac{\sin t\cos t}{\sec^2t}+\dfrac{\tan t\sec^2t}{\sec^2t}
\dfrac{\mathrm dw}{\mathrm dt}=\tan t
You might be interested in
ashley is preparing for house riding competition.she has trained her horse for 6 hours and has completed 276 rounds. at what rat
sukhopar [10]

Answer:

46

Step-by-step explanation:

7 0
3 years ago
Qual das inequações seguintes e equivalente à inequação -2x <4?
garik1379 [7]

Answer:

I dont get your question

4 0
3 years ago
Select the correct answer from the drop-down menu.
elena-14-01-66 [18.8K]

Answer:

c. x² - 10x + 25 = 0

Hope this helps!

5 0
3 years ago
Read 2 more answers
Rafael bought a bag of candy that contains 50 pieces. 30 of those pieces4
ludmilkaskok [199]

tell rafel to be careful , he might get diabetes

Step-by-step explanation:

8 0
3 years ago
Please help me , thank you
Mama L [17]

Answer:

b

Step-by-step explanation:

The range are the values that y can take.

From the graph we can see that all defined values of y are below the x- axis

Thus range is y < 0 → b

5 0
3 years ago
Other questions:
  • According to a recent report, customers who shop at a certain online store spend, on average, s1,500 a year at the store. To inv
    10·1 answer
  • Mr. Smith drew an obtuse triangle with side lengths of 4 cm, 6 cm, and 8 cm. In addition to being an obtuse triangle, what kind
    9·1 answer
  • A local culinary market sells ground sumac for $1.25 per ounce and ground thyme for $1.50 per ounce. You want to make a 25-oz se
    14·1 answer
  • How much is 2.billion in fraction form
    10·2 answers
  • Which best describes the relationship between the lines? 2x – y = −7 2x + 4y = 2
    10·2 answers
  • The half-life of the radioactive element unobtanium-43 is 10 seconds. If 48 grams of unobtanium-43 are initially present, how ma
    13·1 answer
  • Supplementary angles are two angles whose measures have a sum of 180∘. What is the value of x? Write and solve an equation for x
    15·1 answer
  • (05.04 MC) An image of a rectangular pyramid is shown below: A right rectangular pyramid is shown. Part A: A cross section of th
    6·1 answer
  • Please help me I need the answer for this question. correct one please
    12·1 answer
  • Helpppppp now plzzzzzzzzz
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!