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amy0799
 one year ago
if f(x) = 4/(x2), find f'(x)
amy0799
 one year ago
if f(x) = 4/(x2), find f'(x)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i am guessing that this is the very beginning of calc and you have to do with by hand, not using any shortcuts am i right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0next week you will say \[f'(x)=\frac{4}{(x2)^2}\] in your head, but i guess we can take the steps (long and arduous steps)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we will have to go nice an slow first write the definition, then use some algebra ok a lot of algebra it is 99% algebra

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0did you get to \[\huge \lim_{h\to 0}\frac{\frac{4}{(x+h2)}\frac{4}{x2}}{h}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok now in order to spare some agony lets forget about the h in the denominator, and forget about the limit we will deal with those last, ok?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the algebra we need is to (carefully) do this subraction \[\frac{4}{x+h2}\frac{4}{x2}\]

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0(4(x2)4(x+h2))/((x2)(x+h2) is that right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you do this? leave the denominator in factored form i.e don't multiply out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes that is correct now carefully multiply out in the numerator and combine like terms

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0(4x4x8+84h)/((x2)(x+h2))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok that is multiplying out what is left in the numerator?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now recall there is an \(h\) in the denominator cancel it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now 'take the limit as h goes to zero" which is a fancy way of saying erase that h what is left?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0as promised (see above)
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