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 Thread Tools Display Modes 04-29-2013 #1 choiminho   Join Date: Apr 2013 Posts: 1 First Principle of Derivative and Power Rule using the first principle of differentiation, find the first derivatives of 1.f(x) = 3/x^2 2. 1/(sqrt x)^3 -i don't know how to using limit to solve this. Please help me.    04-30-2013   #2
MAS1   Join Date: Dec 2008
Posts: 249 Quote:
 Originally Posted by choiminho using the first principle of differentiation, find the first derivatives of 1.f(x) = 3/x^2 2. 1/(sqrt x)^3 -i don't know how to using limit to solve this. Please help me. 1. Using the quotient rule to solve:

f'(x) = ((derivative of the top)(bottom) - (top)(derivative of the bottom))/(bottom squared)

f'(x) = ((0)(x^2) - (3)(2x))/(x^4) = -6x/x^4 = -6/x^3

Using the product rule to solve:

3/x^2 = 3x^-2

f'(x) = (derivative of first)(second) + (first)(derivative of second)
f'(x) = (0)(x^-2) + (3)(-2x^-3) = -6x^-3 = -6/x^3

Using limit method:

limit as h goes to 0 of (3/(x+h)^2 - 3/x^2)/h = ((3x^2 - 3(x + h)^2)/((x^2)(x + h)^2))/h
= (3x^2 - 3x^2 - 6xh - 3h^2)/((h)(x + h)^2(x^2))
= (-3h(2x + h))/((h)(x + h)^2(x^2))
= (-3(2x + h))/((x + h)^2(x^2))

Now take the limit as h goes to 0.

= (-6x)/(x^4) = -6/x^3

2. f(x) = 1/(sqrt x)^3 = (sqrt(x))^-3 = (x^(1/2))^-3 = x^(-3/2)

f'(x) = (-3/2)(x^(-3/2 - 1) = (-3/2)(x^(-5/2) = -3/(2(sqrt(x))^5)

Last edited by MAS1; 04-30-2013 at 10:48 AM.. Reason: Adding limit method   05-01-2013 #3 mercedes89   Join Date: Mar 2013 Posts: 2 sorry sorry i don't now that you out of luck  Thread Tools Show Printable Version Email this Page Display Modes Switch to Linear Mode Hybrid Mode Switch to Threaded Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
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