Question

Find the derivative of the limit process:
f(x)=8/(x-3) Apparently I've forgotten how to do math soo I'm stuck evaluating this here:
lim Δx->0 ((8/x+Δx-3) - (8/x-3))/Δx

Answer 1

differentials calculus??

Answer 2

\[f(x)=\frac{8}{x-3}; \ \ f(x+h)=\frac{8}{x+h-3}\]

\begin{align}
\lim_{h->0}&\frac{f(x+h)-f(x)}{h}\\\\
&\frac{\cfrac{8}{x+h-3}-\cfrac{8}{x-3}}{h}\\\\
&\frac{\cfrac{8(x-3)-8(x+h-3)}{(x+h-3)(x-3)}}{h}\\\\
&\frac{8(x-3)-8(x+h-3)}{(x+h-3)(x-3)(h)}\\\\
&\frac{8x-24-8x-8h+24}{(x+h-3)(x-3)(h)}\\\\
&\frac{-8h}{(x+h-3)(x-3)(h)}\\\\
&\frac{-8}{(x+h-3)(x-3)}\\\\
&\frac{-8}{(x+0-3)(x-3)}\\\\
&\frac{-8}{(x-3)^2}\\\\
\end{align}

Answer 3

what did i miss?

Answer 4

\[\lim_{\Delta x \rightarrow 0}\frac{\frac{8}{x+\Delta x-3}-\frac{8}{x-3}}{\Delta x} \]

Answer 5

wait it didn't show all that just a sec ago
openstudy is going so slow tonight

Answer 6

8 -8*1
Dx ------ = -------- ... nothing l0ol
(x-3) (x-3)^2

Answer 7

im a ninja ;)

Answer 8

haha

Answer 9

Thank you so much! Any website I can use to practice simple math. I'm so rusty and it will be my downfall on my first calc exam.

Answer 10

you can practice here..

Answer 11

And give ppl wrong answers ._.

Answer 12

interactmath.com