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

F(x) = Y = 4/sqrt(X) = 4/X^(1/2),
Y = 4X^(1/2),
Y'=2X^(1/21) = 2X^(3/2= 2/X^(3/2)= 2/sqrt(X^3). 
using the limit process how do i find the derivative of f(x)=4/sqrt of x?

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
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