cal

posted by .

Find the derivative of the function.

f(x)= x^8√5-3x

  • cal -

    f(x)= x^8√5-3x
    f'(x) = 8x^7√5-3

  • cal -

    but the ans is f(x)= x^7(80-51x)/2√5-3x

  • cal -

    If you mean f(x) = x^8√(5-3x), then
    f'(x)
    = (8x^7)*√(5-3x) + (-3/2)*(x^8) / √(5-3x)

  • cal -

    am lost

  • cal -

    Recall the chain rule. If two expressions which are functions of x are multiplied, we do the following:
    h(x) = f(x)*g(x)
    h'(x) = f'(x)*g(x) + f(x)*g'(x)
    As we can see, the derivative of h(x) is the derivative of f(x) multiplied by the original g(x), plus the derivative of g(x) multiplied by the original f(x).
    For example,
    h(x) = 2x * ln(x)
    We know that
    derivative of 2x = 2, and
    derivative of ln(x) = 1/x. Thus
    h'(x) = 2*ln(x) + (2x)*(1/x)

    In the problem, f(x) = x^8√(5-3x). We can rewrite this as,
    f(x) = (x^8) * (5-3x)^(1/2)
    We know that
    the derivative of x^8 = 8x^7
    the derivative of (5-3x)^(1/2) = (1/2)(-3)(5-3x)^(-1/2)
    Using chain rule, you'll get
    f'(x) = (8x^7)*(5-3x)^(1/2) + (x^8)*(-3/2)*(5-3x)^(-1/2)
    If you simplify this, you'll get the answer that you typed in there:
    f'(x) = x^7(80-51x) / 2√(5-3x)

    Hope this helps :)

  • cal -

    thanks jai

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus derivatives

    f(a) = a + √a (a) Find the derivative of the function using the definition of derivative.
  2. Math

    Find an equation of the line that bisects the obtuse angles formed by the lines with equations 3x-y=1 and x+y=-2. a. (3√2 +√10)x-(√10 + √2)y-2√10+√2=0 b. (3√2 - √10)x+(√10 - √2)y+2√10+√2=0 …
  3. Calculus

    y=(√x)/((√x)+1) Find the concavity and point of inflection(s). y'=1/(√(x/2))(√x+1)² y'=1/(x√(x/2)+2√(x²/2)+√(x/2)) y"=0- ?
  4. Calculus. I need help!

    Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx. y=√sinx √ is square root.
  5. cal

    Find the derivative of y with respect to x,t, or theta, as appropriate. y = ∫ ^(√4x) ^basedown√x (ln(t^2)) dt
  6. CAL

    Hi, im lost in theses three problems. Please help. Thank you so much!!! 1. Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = 3 squareroot all 1 + 5x (g(x), …
  7. CAL

    The _____________ of a function is a formula for the slope of the tangent line to that function at any point x. When the function is defined as f(x), the derivative will be written as __________or ________. When the function is written …
  8. calculus

    (i know i've asked so many questions. i just want to make sure my answers are right for this homework! hopefully it isn't too annoying for you :) ) Find the derivative of the given function. y=(tan^-1)√(3x) A. (1)/(√(1-3x)) …
  9. 8th grade algebra

    Can you check my answers? 1. 3√20/√4 = 3√(5)(4)/2 = 3(2)√5/2 = 3√5 2. 4√15/√9 = 4√15/3 3. √12/√16 = √4(3)/4 = 2√3/4 = √3/2 4. √10/√5 = √2
  10. Math

    Could I please get some help for these 3 questions, apologies for asking so many, but they were the ones I was really unsure of: 1. Find an equation for the line tangent to y=ln(x) and that goes through the origin. I have no idea, …

More Similar Questions