Question

f(x)=1/2e^x

Answer 1

\[f(x)=\frac{ 1 }{2 }e^{x}\]

Answer 2

If you're deriving f(x), the nice thing about e^x is that the derivative of that is itself

So if \[\Large f(x) = e^{x}\], then \[\Large f^{\prime}(x) = e^{x}\]

Answer 3

dun dun dun...jk lol

Answer 4

So the 1/2 means nothing?

Answer 5

so if you have the constant out front, it makes no difference (because you pull that out when you derive anyway)

Answer 6

that means

\[\Large f(x) = \frac{ 1 }{2 }e^{x}\], then \[\Large f^{\prime}(x) = \frac{ 1 }{2 }e^{x}\]

Answer 7

so the derivative is simply 1/2 e^x ....literally the same thing?

Answer 8

exactly, that's why e^x is a very handy function in calculus

Answer 9

well thats crazy

Answer 10

essentially, the rate of growth at any point on f(x) = e^x is exactly equal to e^x

Answer 11

so that's probably where the whole constant came from anyway (not entirely sure though)

Answer 12

hopefully they're all e^x questions because they aren't so bad once you know how to work them

Answer 13

well that's why you have OS lol, so you can ask when you get stuck