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...dans

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Sep 24, 2012
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3
find the derivative of the following functions from 1st principles 1) f(x)= -2x^3

2)f(x)=3sqrt[x]

3)f(x)=(x+1)^2
 
my bad

oh my bad sry nw read the part abt homework, im getting stuck at lim h:0 (-4x^3-6x^2h-6xh^2-2h3)/h
how do i cancel the h??
 
If you still have an x^3 in your numerator, you got lost somewhere in the algebra. Try again.
 
oh my bad sry nw read the part abt homework,
im getting stuck at lim h:0 (-4x^3-6x^2h-6xh^2-2h3)/h
how do i cancel the h??

Please spell out your words, as opposed to typing in textspeak.


\(\displaystyle \dfrac{f(x + h) \ - \ f(x)}{h} \)


\(\displaystyle \dfrac{-2(x + h)^3 \ - \ (-2x^3)}{h}\)


\(\displaystyle \dfrac{-2(x^3 + 3x^2h + 3xh^2 + h^3) + 2x^3}{h} \)


\(\displaystyle \dfrac{-2x^3 - 6x^2h - 6xh^2 - 2h^3 + 2x^3}{h} \)


\(\displaystyle \dfrac{-6x^2h - 6xh^2 - 2h^3}{h} \)


Factor out a common h:


\(\displaystyle \dfrac{h(-6x^2 - 6xh - 2h^2)}{h}\)



Continue . . .




Note:

In front of all of the expressions above there will be the notation
of \(\displaystyle \displaystyle\lim_{h\to 0}.\) In the last couple of
steps (following these), this notation will be dropped.
 
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