## Littlebird one year ago Difference Quotient

1. Littlebird

f(x) = 1/x^4

2. Littlebird

I've managed to get to (-4x^3-6hx^2-4h^2x-h^3)/(x^4*(x+h)^4)

3. triciaal

what do you mean by difference quotient? difference what you get when you subtract quotient what you get when you divide

4. triciaal

|dw:1443157711272:dw|

5. Littlebird

(f(x+h)-f(x))/h

6. gibbs

F

7. misty1212

are you trying to take the derivative by hand ?

8. Littlebird

Yes

9. Littlebird

I know the shortcut

10. misty1212

then you need to compute $\lim_{h\to 0}\frac{1}{(x+h)^4}-\frac{1}{x^4}$ right?

11. gibbs

1 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

12. ytrewqmiswi

u mean the shortcut to find the nth derivative :)

13. misty1212

someone needs to stop @gibbs who clearly does not know what he is talking about

14. Littlebird

yes misty, you have what I wrote, but I also divided everything with h

15. anonymous

Difference Quotient: $$\lim_{h\rightarrow 0} \dfrac{f(x+h) - f(x)}{h}$$

16. ytrewqmiswi

lml he used this XD - http://prntscr.com/8kb4j9

17. anonymous

-_____-

18. anonymous

So 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.

19. misty1212

ok 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

20. misty1212

it is now 100% algebra $\frac{x^4-(x+4)^4}{x^4(x+h)^4}$

21. misty1212

you have no choice here but to expand in the numerator sorry

22. Littlebird

I just noticed that misty put a limit of h->0 next to the thing before If I use that I actually get the answer

23. anonymous

Ugh binomial expansion.

24. misty1212

no choice

25. anonymous

NO choice. you are doomed.

26. Littlebird

(-4x^3-6hx^2-4h^2x-h^3)/(x^4*(x+h)^4)

27. misty1212

ooh k

28. Littlebird

am I normally supposed to have a limit when solving these problems?

29. misty1212

looks like you cancel the $$h$$ to right? so now all that is left is to replace $$h$$ by $$0$$ and you are done

30. misty1212

yes, if you are going to do it by hand

31. anonymous

$\dfrac{x^4-x^4-16x^3 - 96x^2-256x -256}{x^4(x+4)^4}$

32. anonymous

It'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 <_<

33. anonymous

And then you simplify the denominator there at the bottom

34. Littlebird

I already had it expanded. the only thing i was missing was the limit

35. Littlebird

you dont have to do all of this ;)

36. Littlebird

but thankyou

37. anonymous

Why have you multiplied h to the numerator portion? $$\color{#0cbb34}{\text{Originally Posted by}}$$ @Littlebird $$\color{red}{(-4x^3-6hx^2-4h^2x-h^3)}/(x^4*(x+h)^4) \(\color{#0cbb34}{\text{End of Quote}}$$ That portion.

38. Littlebird

I 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