Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

JenniferSmart1

  • 2 years ago

why is the derivative of \[(Ax+B)e^x\] \[(Ax+A+B)e^x\]? I understand the Ax+A part, but why didn't the B disappear? btw it's an ODE problem. \[y''-4y=xe^x+cos2x\]

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

    \[y=(Ax+B)e^x\]\[y'=(Ax+B)e^x+Ae^x=(Ax+A+B)e^x\]

  2. JenniferSmart1
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how odd, wolfram alpha won't show me the steps unless I sign up with them.

  3. JenniferSmart1
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    why doesn't the B disappear? Isn't it a constant?

  4. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    derivative of B * e^x is B* d/dx (e^x) = B* e^x

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

    By the product rule the B disappears from one Ax+B term, and in the other term you differentiate e^x \[u=Ax+B\]\[u'=A\]\[v=e^x\]\[v'=e^x\]\[uv'+vu'=(Ax+B)e^x+Ae^x\]factor out \(e^x\) and you get\[(Ax+A+B)e^x\]

  6. JenniferSmart1
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    awesome thanks!!!!

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

    • 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.