how to solve this in the shortest way?
finding the 10th derivative

- anonymous

how to solve this in the shortest way?
finding the 10th derivative

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- anonymous

find the 10th derivative of the function

- ganeshie8

hmm why are u posting q in installments

- anonymous

|dw:1433233107942:dw|

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## More answers

- ganeshie8

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

- ganeshie8

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

- anonymous

i will just derive the x10?

- ganeshie8

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

- ganeshie8

x10 doesn't look mathematical
x^10 looks better

- anonymous

ow im sorry ok

- anonymous

x^10 i mean

- ganeshie8

yes just find the 10th derivative of that

- ganeshie8

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

- anonymous

how sir?

- 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

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

- ganeshie8

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

- anonymous

wow. wait i will answer your question the derivative of 1000

- ganeshie8

Awesome! what is it

- anonymous

my calculator says math error

- ganeshie8

lmao

- anonymous

1000! this is the answer right?

- ganeshie8

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

- anonymous

yes yes

- anonymous

am i right?

- ganeshie8

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

- anonymous

but u asked that earlier haha

- anonymous

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

- anonymous

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

- ganeshie8

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

- ganeshie8

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

- ganeshie8

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

- anonymous

|dw:1433234595866:dw|

- anonymous

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

- ganeshie8

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

- anonymous

ooooh i understand now

- anonymous

thanks again sir :-)

- 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

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

this website is a great help for me :-)

- ganeshie8

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

- anonymous

ok sir :-)

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