## anonymous one year ago how to solve this in the shortest way? finding the 10th derivative

1. anonymous

find the 10th derivative of the function

2. ganeshie8

hmm why are u posting q in installments

3. anonymous

|dw:1433233107942:dw|

4. ganeshie8

10th derivative kills all the terms having exponent 9 and below

5. ganeshie8

so forget about all the terms except first |dw:1433233262560:dw|

6. anonymous

i will just derive the x10?

7. ganeshie8

since you're doing calculus, it is time to use proper notation use ^ for exponent

8. ganeshie8

x10 doesn't look mathematical x^10 looks better

9. anonymous

ow im sorry ok

10. anonymous

x^10 i mean

11. ganeshie8

yes just find the 10th derivative of that

12. ganeshie8

if you're careful, its not so hard to find a pattern for $$n$$th derivative of $$x^n$$

13. anonymous

how sir?

14. ganeshie8

$$\large \frac{d}{dx}(x^n) = nx^{n-1}$$ $$\large \frac{d^2}{dx^2}(x^n) = n(n-1)x^{n-2}$$ based on that pattern, can you guess $$\large \frac{d^{1000}}{dx^{1000}}(x^n)$$ ?

15. anonymous

i just do the long method is the answer 3628800? is that correct?

16. ganeshie8

Yep! just notice 3628800 = 10*9*8*7*6*5*4*3*2*1 = 10!

17. anonymous

18. ganeshie8

Awesome! what is it

19. anonymous

my calculator says math error

20. ganeshie8

lmao

21. anonymous

1000! this is the answer right?

22. ganeshie8

do you mean $\large \frac{d^{1000}}{dx^{1000}}(x^{1000}) = 1000!$

23. anonymous

yes yes

24. anonymous

am i right?

25. ganeshie8

Looks good! thats not exactly same as the question i have asked but ok

26. anonymous

but u asked that earlier haha

27. anonymous

|dw:1433234272561:dw| is this equation true to all functions sir?

28. anonymous

can i use this everytime the question asks find the nth derivative?

29. ganeshie8

sorry thats a confusing notation... very wrong acttually, my mistake

30. ganeshie8

Here it is : If $$\large f(x) = x^n$$, then the $$n$$th derivative is $$\large n!$$

31. ganeshie8

If $$\large f(x) = x^k$$, then the $$k$$th derivative is $$\large k!$$ btw $$k,n$$ are posiitve integers

32. anonymous

|dw:1433234595866:dw|

33. anonymous

so everytime i encounter this kind of question,, i will only leave x^10? just the first term?

34. ganeshie8

If you're formula oriented, then yes just do that

35. anonymous

ooooh i understand now

36. anonymous

thanks again sir :-)

37. ganeshie8

np :) maybe work it the long way once to see why all those terms with lesser exponents don't matter for 10th derivative

38. anonymous

i have here many questions because i am now in my final year of engineering. that's why. so i must answer all these questions. so that i can graduate. thanks a lot sir.

39. anonymous

this website is a great help for me :-)

40. ganeshie8

ikr there is never enough time to do all the things! feel free to tag me in your future questions.. good luck!

41. anonymous

ok sir :-)