Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

calyne

  • 4 years ago

Use logarithmic differentiation to find the derivative of the function y = (cosx)^x

  • This Question is Closed
  1. mf1021
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    take the log both sides. lny=xln(cosx)

  2. mf1021
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    and take derivative both sides

  3. mf1021
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    y prime/y= (ln(cosx))+x(1/cosx)(-sinx) and isolate y prime and you are done

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

    \[\int\limits \text{Cos}[x]^x (\text{Log}[\text{Cos}[x]]-x \text{Tan}[x])dx = \text{Cos}[x]^x \]

  5. Ayesha1603
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    put ln on both sides to get \[\ln y =x \ln cosx\] then differentiate to get \[1/y =1\times -sinx\]

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

    also you can use formula for logarithmic differentiation... d/dx(u^v)=u^v*d/dx(v*log u )

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy