Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

richyw Group Title

having a little bit of trouble remembering how to do the differential.

  • one year ago
  • one year ago

  • This Question is Closed
  1. richyw Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so I have \(k(x,y,z)=e^{x^2+y^2+z^2}\) where \(x=\sqrt{t+1},\;y=\sqrt{t^2+1},\:z=\sqrt{t^3+1}\) . Now i need to find \(\frac{dk}{dt}\).

    • one year ago
  2. richyw Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    to do this do I just say\[\frac{dk}{dt}=\frac{dk}{dx}\frac{dx}{dt}+\frac{dk}{dy}\frac{dy}{dt}+\frac{dk}{dz}\frac{dz}{dt}\]

    • one year ago
  3. richyw Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I am getting an answer of \[\frac{dk}{dt}=2e^{t^3+t^2+t+3}\left(3t^2+2t+1\right)\] is this correct, and does anyone know how to check this on wolfram, or open-source math software?

    • one year ago
  4. eseidl Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The formula for the total differential is correct, as long as the dk/dx,etc terms are partial derivatives.

    • one year ago
  5. richyw Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah sorry I didn't want to type "partial" \(\partial\) in the latex that many times :)

    • one year ago
  6. richyw Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks a lot. can anyone confirm this is the correct answer?

    • one year ago
  7. eseidl Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    this one is super tedious...give me a minute I'll do it with pen and paper...

    • one year ago
  8. richyw Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    alright thanks a lot. I really appreciate it.

    • one year ago
  9. eseidl Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I get:\[e^{t^3+t^2+t+3}(3t^2+2t+1)\]

    • one year ago
  10. eseidl Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Your factor of two should cancel when you differentiate the square root term (which gives you a 2 in the denominator)...

    • one year ago
  11. richyw Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks a lot! I see I made a basic calculus mistake but am glad I remember this stuff!

    • one year ago
    • Attachments:

See more questions >>>

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.