anonymous
  • anonymous
how to solve this in the shortest way? finding the 10th derivative
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
find the 10th derivative of the function
ganeshie8
  • ganeshie8
hmm why are u posting q in installments
anonymous
  • anonymous
|dw:1433233107942:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

ganeshie8
  • ganeshie8
10th derivative kills all the terms having exponent 9 and below
ganeshie8
  • ganeshie8
so forget about all the terms except first |dw:1433233262560:dw|
anonymous
  • anonymous
i will just derive the x10?
ganeshie8
  • ganeshie8
since you're doing calculus, it is time to use proper notation use ^ for exponent
ganeshie8
  • ganeshie8
x10 doesn't look mathematical x^10 looks better
anonymous
  • anonymous
ow im sorry ok
anonymous
  • anonymous
x^10 i mean
ganeshie8
  • ganeshie8
yes just find the 10th derivative of that
ganeshie8
  • ganeshie8
if you're careful, its not so hard to find a pattern for \(n\)th derivative of \(x^n\)
anonymous
  • anonymous
how sir?
ganeshie8
  • 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 \(\large \frac{d^{1000}}{dx^{1000}}(x^n)\) ?
anonymous
  • anonymous
i just do the long method is the answer 3628800? is that correct?
ganeshie8
  • ganeshie8
Yep! just notice 3628800 = 10*9*8*7*6*5*4*3*2*1 = 10!
anonymous
  • anonymous
wow. wait i will answer your question the derivative of 1000
ganeshie8
  • ganeshie8
Awesome! what is it
anonymous
  • anonymous
my calculator says math error
ganeshie8
  • ganeshie8
lmao
anonymous
  • anonymous
1000! this is the answer right?
ganeshie8
  • ganeshie8
do you mean \[\large \frac{d^{1000}}{dx^{1000}}(x^{1000}) = 1000!\]
anonymous
  • anonymous
yes yes
anonymous
  • anonymous
am i right?
ganeshie8
  • ganeshie8
Looks good! thats not exactly same as the question i have asked but ok
anonymous
  • anonymous
but u asked that earlier haha
anonymous
  • anonymous
|dw:1433234272561:dw| is this equation true to all functions sir?
anonymous
  • anonymous
can i use this everytime the question asks find the nth derivative?
ganeshie8
  • ganeshie8
sorry thats a confusing notation... very wrong acttually, my mistake
ganeshie8
  • ganeshie8
Here it is : If \(\large f(x) = x^n\), then the \(n\)th derivative is \(\large n!\)
ganeshie8
  • ganeshie8
If \(\large f(x) = x^k\), then the \(k\)th derivative is \(\large k!\) btw \(k,n\) are posiitve integers
anonymous
  • anonymous
|dw:1433234595866:dw|
anonymous
  • anonymous
so everytime i encounter this kind of question,, i will only leave x^10? just the first term?
ganeshie8
  • ganeshie8
If you're formula oriented, then yes just do that
anonymous
  • anonymous
ooooh i understand now
anonymous
  • anonymous
thanks again sir :-)
ganeshie8
  • ganeshie8
np :) maybe work it the long way once to see why all those terms with lesser exponents don't matter for 10th derivative
anonymous
  • 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.
anonymous
  • anonymous
this website is a great help for me :-)
ganeshie8
  • ganeshie8
ikr there is never enough time to do all the things! feel free to tag me in your future questions.. good luck!
anonymous
  • anonymous
ok sir :-)

Looking for something else?

Not the answer you are looking for? Search for more explanations.