posted by .

find the derivative of y =(x+3)^3 / sqrt(x^2 -1) using logarithmic differentation.

  • Calc -

    y =(x+3)^3 / √(x^2 -1)
    lny = 3ln(x+3) - 1/2 ln(x^2-1)
    1/y y' = 3/(x+3) - x/(x^2-1)
    1/y y' = (3(x^2-1) - x(x+3))/((x+3)(x^2-1))
    1/y y' = (2x^2-3x-3)/((x+3)(x^2-1))

    y' = (x+3)^3 / √(x^2 -1) * ((2x^2-3x-3)/((x+3)(x^2-1)))
    = ((x+3)^2 * (2x^2-3x-3))/(x^2-1)^(3/2)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc

    find the derivative of y = sqrt(9 - 16x) Use the chain rule. First find the derivative of the sqrt, and multiply that by the derivative of what is contained inside. Cake. Use the chain rule. If we have y(x)=sqrt(9-16x) then y'=d/dx(sqrt(9-16x))*d/dx(9-16x) …
  2. finding c: calc

    let f(x)=square root x. if the rate of change of at x=c is twice its rate of change at x=1, then c=?
  3. Calc

    Can anyone help me find the derivative of these functions?
  4. calc

    logarithmic differentiation of find derivative of y= square root of x^x
  5. calc

    find derivative using limit definition: f(x) = x - sqrt(x) so f'(x) = lim h->0 [f(x+h) - f(x)]/h but I keep trying to solve by multiplying by the conjugate but I can't figure it out..there's nothing that can be cancelled or anything …
  6. Calc

    Compute the derivative of f(x)=5^x^2+1 using logarithmic differentiation.
  7. Calc I

    if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t-1)^-1/2 * 4t^3 and i'm trying to figure out if i need the product rule again to find the second derivative -1t^3(4t-1)^-3/2 * 4t^3 The answer if -4/27 and I'm …
  8. calc

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

    Use logarithmic differentiation to find the derivative of the function. y =sqrt(x)^3x
  10. math please help!!

    For what values of x is the graph of y = 8e^−x^2 concave down?

More Similar Questions