math

posted by .

Let
f(x)=((x^(6))*((x-8)^(2)))/((x2+4)^(7))
Use logarithmic differentiation to determine the derivative.
f '(x) =
f '(8) =

  • math -

    ln f = ln(x^6) + ln(x-8)^2 - ln(x^2+4)^7
    = 6ln(x) + 2ln(x-8) - 7ln(x^2+4)
    1/f f' = d/dx 6ln(x) + 2ln(x-8) - 7ln(x^2+4)

    f ' = (6/x + 2/(x-8) - 14x/(x^2+4)) * (x^6 * (x-8)^2) / (x^2+4)^7

    you can massage that in various ways. One way ends up as

    -2(x-8)(x^5)(3x^3-32x^2-16x+96)/(x^2+4)^8

    plug in x=8 to get the value. That (x-8) in the numerator makes it all 0.

  • math - PS -

    Actually, if you hadn't been asked for f '(x), you could have saved all the work by noting that if (x-k)^n is a factor of f(x), and n > 1, then (x-k) will be a factor of each term of f '(x), so f '(k) will be zero.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    I need to find the derivative of the following problem via logarithmic differentiation, but I'm getting stuck. I know how to solve via logarithmic differentiation, but I can't figure out how to re-write the exponent(s) as logs. Could …
  2. Calculus

    Use logarithmic differentiation to determine the derivative of the function defined by f(x)=x^5(x-3)^9/(x^2+2)^4
  3. Math

    f(x)=x^5x Use logarithmic differentiation to determine the derivative.
  4. Calculus Help

    Use logarithmic differentiation to find the derivative of the function. y = (tan x)^(7/x)
  5. math

    Use logarithmic differentiation to find the derivative of the function. y = (cos 2x)x
  6. calc

    Use logarithmic differentiation to find the derivative of the function. y = (x^4 + 2)^2(x^3 + 4)^4
  7. math

    Use logarithmic differentiation to find the derivative of the function. y = (x^4 + 2)^2(x^3 + 4)^4
  8. Calculus 1

    Use logarithmic differentiation to find the derivative of the function. y = x^(8cosx)
  9. Calculus 1

    Use logarithmic differentiation to find the derivative of the function. y =sqrt(x)^3x
  10. Math

    Use logarithmic differentiation to find the derivative of y: y=x^(e^x)

More Similar Questions