calculus

posted by .

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

• calculus -

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).

• calculus -

using the limit process how do i find the derivative of f(x)=4/sqrt of x?

• calculus -

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

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 ã3x …
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 ã3x …
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 /3x …
4. 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?
5. Calculus

Could someone please help me with these questions;I was having trouble with these four questions. Evaluate each limit, if it exists, using any appropriate technique. 1.) The limit as u approaches 4; u^2-16/u^3-64 2.) The limit as x …
6. calculus

Find the derivative using the limit process y=cox find dy/dx
7. calculus

6. What is the derivative of y = square root of 3x ?
8. Calculus

I am not sure what to do here: Find the derivative (f '(x) using the limit process a). f(x)= 2x^2+5x+2 find f ' (2) b.) Find the equation of the Tangent Line at (1,5)
9. Calculus

1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^-1 x is 1/(|x|*sqrt(x^2 -1)). …
10. Math (derivative by limit process)

Find the derivative of the function by the limit process. f(x)=1/sqrt(x) I've worked through my problem and got f'(x) to be -1/2x but the actual answer is -1/2x^3/2?

More Similar Questions