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

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

Mathematics
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find the 10th derivative of the function
hmm why are u posting q in installments
|dw:1433233107942:dw|

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

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