Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathstina

  • 2 years ago

Find the directional derivatives of the following functions at the given points P in the direction of the vectors v. f(x,y,z) =√xyz , P (3,2,6) , v =<-1,-2,2>

  • This Question is Closed
  1. piscez.in
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    find the derivatives of the function x, y and z seperately, by keeping the other 2 variables constant in each case. Think of a smart way to keep the other 2 variables constant!

  2. mathstina
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, i tried to work out. is the ans -1?

  3. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is you function?\[f(x,y,z)=\sqrt{xyz}\]or\[f(x,y,z)=\sqrt xyz\]?

  4. mathstina
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the first one

  5. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[D_{\vec v}=\nabla f(3,2,6)\cdot\frac{\vec v}{\|\vec v\|}\]I don't think the answer is one but I haven't done it yet...

  6. Algebraic!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is there an advanced equation editor available to super users that has cool features like gradient?

  7. mathstina
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    negative one

  8. piscez.in
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathstina @TuringTest is right

  9. piscez.in
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathstina first fing the derivative of the function with respect to x, by substituting the y and x values

  10. mathstina
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  11. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh yeah, I do get -1 :)

  12. mathstina
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok thanks a lot!

  13. piscez.in
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @TuringTest @mathstina no its not -1, atleast as per my calculations

  14. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I will show my work and you can spot a mistake if you see one...

  15. piscez.in
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  16. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\nabla f=\frac12\langle\sqrt{\frac{yz}x},\sqrt{\frac{xz}y},\sqrt{\frac{xy}z}\rangle\implies\nabla f(3,2,6)=\frac12\langle2,3,1\rangle\]\[\frac{\vec v}{\|\vec v\|}=\frac13\langle-1,-2,2\rangle\]\[\nabla f(3,2,6)\cdot\frac{\vec v}{\|\vec v\|}=\frac16(-2-6+2)=-1\]

  17. mathstina
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Great!

  18. piscez.in
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @TuringTest @mathstina im sorry, your right, i made a mistake by putting all -ves as +ves and vice versa. Bravo you two

  19. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    cheers!

  20. mathstina
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Its ok. u too got the same ans

  21. piscez.in
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i got it as 1 previously, now i have -1 :)

  22. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.