# calculus

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

1. 👍 0
2. 👎 0
3. 👁 366
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
2. using the limit process how do i find the derivative of f(x)=4/sqrt of x?

1. 👍 0
2. 👎 0
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

## Similar Questions

1. ### Math ~CHECK MY ANSWER~

1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? a. Square root 120 , n , Square root 3

2. ### Math

1. Rosa, Roberto, Andrea, and Inno find an estimate for square root 10. Who has proposed the best solution? (1 point) Rosa: "Use square root 9 and square root 25 to estimate." Roberto: "I will use square root 4 and square root 9."

3. ### Math

1. Which of the following numbers is a rational? A. 4/5 B. square root of 27 C. 4.02002000200002... **** D. Square root of 31 2. Which type of number is shown below? 0.313311333111... A. repeating decimal B. rational C. irrational

4. ### math

Four students work to find an estimate for square root 54. Who is closest to finding the true estimate? (1 point) Rhonda: "Use square root 16 and square root 25 to estimate." Ricardo: "I use square root 25 and square root 36."

1. ### 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

2. ### algebra

Which shows the expressions in the order they would appear on a number line from least to greatest? 17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3 3 to the power of 3, square root of 30,

3. ### math

1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? a. Square root 120 , n , Square root 3

4. ### Calculus

A rectangle is bounded by the x axis and the semicircle = square root 25-x^2. What length and width should the rectangle have so that its area is a maximum? When I worked the problem out(which is a bit detailed). I started with y

1. ### Algebra

Use the quadratic formula to solve the equation. Give exact answers: 2x^2 -1 = 6x. The choices are: a) -3 + square root(7)/2, -3 - square root(7)/2 b) 3 + square root(11)/2, 3 - square root(11)/2 c) 3 + square root(7)/2, 3 -