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Littlebird
 one year ago
Difference Quotient
Littlebird
 one year ago
Difference Quotient

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Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0I've managed to get to (4x^36hx^24h^2xh^3)/(x^4*(x+h)^4)

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0what do you mean by difference quotient? difference what you get when you subtract quotient what you get when you divide

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443157711272:dw

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1are you trying to take the derivative by hand ?

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0I know the shortcut

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1then you need to compute \[\lim_{h\to 0}\frac{1}{(x+h)^4}\frac{1}{x^4}\] right?

gibbs
 one year ago
Best ResponseYou've already chosen the best response.01 Factor out the common term f f(x+h−x)/h 2 Gather like terms f((x−x)+h)/h 3 Simplify (x−x)+h to h fh/h 4. Cancel h f

ytrewqmiswi
 one year ago
Best ResponseYou've already chosen the best response.0u mean the shortcut to find the nth derivative :)

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1someone needs to stop @gibbs who clearly does not know what he is talking about

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0yes misty, you have what I wrote, but I also divided everything with h

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0Difference Quotient: \(\lim_{h\rightarrow 0} \dfrac{f(x+h)  f(x)}{h}\)

ytrewqmiswi
 one year ago
Best ResponseYou've already chosen the best response.0lml he used this XD  http://prntscr.com/8kb4j9

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0So find all the hard stuff first: \(f(x+h) = \dfrac{1}{(x+h)^4}\) put it back into the formula : \(\dfrac{\dfrac{1}{(x+h)^4}  \dfrac{1}{x^4}}{h}\) Then start simplifying by finding a common denominator in the numerator portion.

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1ok leave out the \(h\) in the denominator for a moment and focus just on \[\frac{1}{(x+h)^4}\frac{1}{x^4}\] we will divide by ]\(h\) at the end

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1it is now 100% algebra \[\frac{x^4(x+4)^4}{x^4(x+h)^4}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1you have no choice here but to expand in the numerator sorry

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0I just noticed that misty put a limit of h>0 next to the thing before If I use that I actually get the answer

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0Ugh binomial expansion.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0NO choice. you are doomed.

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0(4x^36hx^24h^2xh^3)/(x^4*(x+h)^4)

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0am I normally supposed to have a limit when solving these problems?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1looks like you cancel the \(h\) to right? so now all that is left is to replace \(h\) by \(0\) and you are done

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1yes, if you are going to do it by hand

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0\[\dfrac{x^4x^416x^3  96x^2256x 256}{x^4(x+4)^4}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0It's just too much to constantly write the limit over and over again in latex, so i just leave it for the end... it's wrong but <_<

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0And then you simplify the denominator there at the bottom

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0I already had it expanded. the only thing i was missing was the limit

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0you dont have to do all of this ;)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0Why have you multiplied h to the numerator portion? \(\color{#0cbb34}{\text{Originally Posted by}}\) @Littlebird \(\color{red}{(4x^36hx^24h^2xh^3)}/(x^4*(x+h)^4) \(\color{#0cbb34}{\text{End of Quote}}\) That portion.

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0I multiplied both the top and bottom of the fraction by x^4(x+h)^4 so that I could make the fractions on top go away
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