A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

find the derivative of g(x)= 4sqrt(x)+3

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

    is it just sqrtx

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

    \[\large{g'(x) =4 \times \frac{1}{2} x^{\frac{-1}{2}}} = \frac{2}{\sqrt{x}}\]

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

    i think it would be 2/sqrt(x)

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

    first convert the square root to a fractional index = 4x^(1/2) + 3 derivative = 4 * (1/2) x ^(1/2 - 1) = 2 x(-1/2) or 2 / sqrtx

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

    why did you have (1/2-1)...where did the -1 come from?

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

    we used the general formula for the derivative of if f(x) = ax^n f'(x) = an x^(n-1)

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

    oh ok thanks

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

    yw

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

    jimmy could you help me with this one...its confusing. A girl standing on the top of a building 200 feet highs throws a water balloon up in the air at a velocity of 30ft/sec. The equation for the height of the water balloon is h(t)=-16t^2 +30t + 200 find the instantaneous velocity at two seconds and the direction of the water balloon

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

    instantaneous velocity is dh/dt take the derivative with respect to t to get a new equation then sub in t=2 to find the velocity

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

    if you get +, the balloon is going higher. if you get a negative number, the balloon is falling

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

    can someone please demonstrate that

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

    find the derivative term by term use if f(t) = a*t^n f'(t) = a*n* t^(n-1) just like Jim did up above

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

    h(t)=-16t^2 +30t + 200 first find the derivative of -16 t^2 using the rule

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

    -32t + 30t + 0??

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

    check derivative of 30t

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

    30t is already reduce, isnt it?

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

    you start with -16t^2 +30t + 200 then term by term 2* -16 * t^ (2-1) 30*1* t^(1-1) 200 * 0 * t(0-1)

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

    remember t^0 is 1

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

    oh i see so when i have -32t + 1 + 0...do i just plug in 2 to find the instantaneous velocity into t

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

    of course nobody uses the exponent rule to find the derivative of a constant. We know it is zero.

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

    now recheck : derivative with respect to t of : 30 t = ??

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

    t^0= 1 therefore, 30t = 1?

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

    use the rule: d/dt (30 t^1) = 1*30*t^(1-1) = 1*30*1 = ??

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

    just 30

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

    so the derivative of -16t^2 +30t + 200 = ?

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

    -32t + 30 + 0

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

    adding 0 is not usually done . I mean leave it off, because it does not change anything

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

    so now you have h'(t) = -32t + 30 change in height with respect to time (velocity for this problem= -32t + 30

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

    find the instantaneous velocity at two seconds and the direction of the water balloon this means replace t with 2 in your equation to find the velocity at time t=2

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

    ok i did and i got -34

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

    you got -34 ft/sec (don't forget the units) the negative sign means which direction? Here is how we know which direction: A girl throws a water balloon *up* in the air at a velocity of +30ft/sec. The problem says +30ft/sec is up, so a -34 ft/sec must be which direction?

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

    down

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

    I hope it makes sense. But you have answered the entire question.

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

    yeah it really did. thanks for taking the time.

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

    to teach me

  37. 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.