Question

Is this correct?

Answer 1

As we know,\(\LARGE \int\limits e^x(f(x)+f'(x))=e^x f(x)\)
So will this be true?
\[\LARGE \int\limits e^x (f'(x)+f''(x))=e^x (f'(x))\]
Just a thought..

Answer 2

@ganeshie8

Answer 3

@terenzreignz @Callisto

Answer 4

ok think about it. f(x) can be anything correct? any function will work. So you could sub in g(x), or h(x), and it is still true.
Can't you sub in any function?

Answer 5

not sure

Answer 6

f means any function, it should be anything
so you can replace f(x) in that formula with anything you want

Answer 7

Come now, all you need to allay your doubts is to differentiate
\[\Large e^xf'(x)\]

Answer 8

so its true??

Answer 9

\[\large e^x f'(x)+e^x f''(x)\]

Answer 10

Assuming that that second derivative does exist, there's no reason I can think of for why it can't be true...

Answer 11

thanks!