calculus

how do I find the derivative of f(x)= 4/ square root of x ? using the limit process?

  1. 👍 0
  2. 👎 0
  3. 👁 150
asked by Terry
  1. F(x) = Y = 4/sqrt(X) = 4/X^(1/2),
    Y = 4X^(-1/2),
    Y'=-2X^(-1/2-1) = -2X^(-3/2= -2/X^(3/2)= -2/sqrt(X^3).

    1. 👍 0
    2. 👎 0
    posted by Henry
  2. using the limit process how do i find the derivative of f(x)=4/sqrt of x?

    1. 👍 0
    2. 👎 0
    posted by Terry
  3. f '(x) = lim [4/√(x+h) - 4/√x]/h as h ---> 0
    = lim [(4√x - 4√(x+h))/(√x√(x+h))*(1/h)*(4√x + 4√(x+h))/(4√x + 4√(x+h))
    = lim [16x - 16(x+h)]/(√x√(x+h)(4√x + 4√(x+h)) * 1/h
    = lim (-16h)/(√x√(x+h)(4√x + 4√(x+h)) * 1/h as h ---> 0
    = -16/(2x(8√x))
    = -1/(x√x) or -1/x^(3/2) or -(x^-(3/2)) or -1/(√x)^3

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Chain Rule

    Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x

    asked by Matt on September 26, 2007
  2. Calculus

    Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x

    asked by Matt on September 30, 2007
  3. Calculus

    Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x

    asked by Matt on September 30, 2007
  4. Math simplifying mixed radicals

    Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn : I don't know how to type a square root sign so I just wrote square root and the numbers infront of the square root are

    asked by Miley on September 14, 2013
  5. Calculus/Logarithms

    Find the derivative of f(x) = (square root of x)(ln x). Using my notes, I came up with f'(x) = (1/2*square root of x)/x The answer in the back of the book says f'(x) = (2+ln x)/(2*square root of x). Can someone please explain how?

    asked by Amy on June 29, 2009
  6. algebra

    1.)correct 2.)wrong---> the first term is wrong 4(3a^2)^2 = 36a^4 3.) not sure on this one 4.) wrong---> - square root of six is not a solution Hope this Helps! 1)find p(-3)if p(x)=4x^3-5x^2+7x-10 =-184 2)If r(x)=4x^2-3x+7,find

    asked by manny on August 16, 2007
  7. Math Help!

    Four students worked to find an estimate for square root 22. Who is closest to finding the true estimate? A. Tiffany: "Use square root 16 and square root 25 to estimate." B. Todd: "I use square root 9 and square root 16." C.

    asked by Laura Ashley on November 3, 2014
  8. College Algebra

    I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth

    asked by Krissy on January 19, 2013
  9. College Algebra help please

    I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth

    asked by Krissy on January 20, 2013
  10. College Algebra

    I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth

    asked by Krissy on January 21, 2013
  11. math

    Four students work to find an estimate for square root 37. Who is closest to finding the true estimate? (1 point) Rhonda: "Use square root 16 and square root 25 to estimate." Ricardo: it should be between square root 25 and square

    asked by lily on November 2, 2016

More Similar Questions