If n = j + k, prove or disprove (d^n /dx^n )f(x) = (d^j /dx^j )((d^k /dx^k )f(x)) = (d^k /dx^k )((d^j /dx^j )f(x))


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Question Number 165044 by alephzero last updated on 25/Jan/22

$If n = j + k, prove or disprove$ $\frac{d^{n}}{{d x}^{n}} f (x) = \frac{d^{j}}{{d x}^{j}} (\frac{d^{k}}{{d x}^{k}} f (x)) = \frac{d^{k}}{{d x}^{k}} (\frac{d^{j}}{{d x}^{j}} f (x))$
Commented by mr W last updated on 25/Jan/22

$t h i s i s t h e s a m e a s$ $n = j + k = k + j$ $y^{(n)} m e a n s d o i n g n t i m e s d e r i v a t i v e,$ $l i k e e a t i n g n a p p l e s . y o u c a n d o k$ $t i m e s a n d t h e n j t i m e s, o r y o u d o j$ $t i m e s a n d t h e n k t i m e s . j u s t l i k e$ $y o u e a t k a p p l e s a t f i r s t a n d t h e n j$ $a p p l e s, {i t}^{'} s t h e s a m e a s y o u e a t j a p p l e s$ $a t f i r s t a n d t h e n k a p p l e s .$
Commented by alephzero last updated on 25/Jan/22

$Thank you, mr W$
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