A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

amy0799

  • one year ago

The function f and g are differentiable at x=10 and x=20 and f(g(x))=x^2. if f(10)=5, f'(10)=4, f'(20)=-5, and g(10)=20, what is the value of g'(10)?

  • This Question is Closed
  1. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    have you used chain rule to differentiate f(g(x)) yet?

  2. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I learned how to do the chain rule

  3. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ok then what is \[\frac{d}{dx}f(g(x))=?\]

  4. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    f(x)g'(x)+g(x)f'(x)

  5. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    that is the product rule we don't have f*g we have f composed with g

  6. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    this is why I asked you to use chain rule to differentiate f(g(x))

  7. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I thought u use the chain rule when its something to a power

  8. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    power rule is what you use when you have a constant power

  9. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    chain rule is what you use when you have a function inside a function

  10. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ooh ok. So how would I do the chain rule for this? would it be f'(g(x))*g'(x)?

  11. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    that is right

  12. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[f(g(x))=x^2 \\ \text{ differentiating both sides } \\ f'(g(x)) \cdot g'(x)=2x\]

  13. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    not enter in 10 for x

  14. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[f'(g(10)) \cdot g'(10)=2(10)\]

  15. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you are given g(10)

  16. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    g(10)=20 right?

  17. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so replace g(10) with 20 \[f'(g(10)) \cdot g'(10)=2(10)\] \[f'(20) \cdot g'(10)=2(10)\]

  18. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    see if you can finish the rest

  19. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    g'(10)=25?

  20. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[f'(20)=-5 \\ \text{ so we have } \\ -5 \cdot g'(10)=2(10)\]

  21. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    hmmm how did you get g'(10)=25?

  22. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh I added, oops

  23. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you do know the operation between -5 and g'(10) is multiplication and not addition :p

  24. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    g'(10)=-4?

  25. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    20/-5 is -4 good worrk

  26. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thank you!

  27. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I have another question, do u mind helping me till?

  28. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I can take a look

  29. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    In the table below, the values of f(x), g(x), f'(x) and g'(x) are given 2 values of x. if y =[f(2x)+g(x)]^2, find y'(3)

  30. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    well we know we are going to have differentiate since we want to find y'(of something)

  31. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1441749521965:dw|

  32. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    again here you will have to use chain rule this chain rule does come with power rule because we have have a constant power we will also have to use sum rule then chain rule again

  33. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2(f(2x)+g(x))*(f'(2x)+g'(x))

  34. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ok I only have one complaint...

  35. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    let's look at f(2x)

  36. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    notice the inside function is 2x

  37. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    the outside function is f( )

  38. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    when you find the derivative of f(2x) w.r.t. x you should get 2*f'(2x) derivative of inside time derivative of outside

  39. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[y(x)=[f(2x)+g(x)]^2 \\ y'(x)=2[f(2x)+g(x)] \cdot [2 f'(2x)+g'(x)]\]

  40. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    now we want to find y'(3)

  41. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so replace x with 3

  42. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\\ y'(3)=2[f(2\cdot 3)+g(3)] \cdot [2 f'(2 \cdot 3)+g'(3)]\]

  43. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y'(3)=112

  44. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[f(6)=? \\ g(3)=? \\ f'(6)=? \\ g'(3)=?\] you found these values from the table ?

  45. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[f(6)=-3 \\ g(3)=-1 \\ f'(6)=-2 \\ g'(3)=-5\] this is what I see for those values is that what you also see

  46. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh I know what I did wrong. Hold on

  47. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y'(3)=72?

  48. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    purrrfect (you know like a cat)

  49. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    haha thank you so much for the help!

  50. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    np I hope everything makes more sense

  51. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yup it does thanks to your help :D

  52. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    np I must go now good luck with calculus

  53. amy0799
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok. thanks, I need all the luck I can get haha

  54. 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

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.