Question

Find a formula for F^(n)(x) if f(x)=e^(2X+1)
f^(n)(x)=?

Answer 1

u mean the generalize derivative of f(x) right ?

Answer 2

i think so.

Answer 3

i think i have to take derivatives like 3 or 4 times and come up with a formula

Answer 4

for this case, we can use the chail rule
f(x)=e^(2X+1) ---> f ' (x) = 1/2 * e^(2X+1)
it is the first derivative

Answer 5

*chain

Answer 6

f '(x)=1/2 * e^(2X+1) --->f '' = 1/2*1/2*e^(2X+1) = (1/2)^2*e^(2x+1)
it is the 2nd derivative

Answer 7

i thought it was this
first derivative 2e^(2x+1)
second 4e^(2x+1)
third 8e^(2x+1)

Answer 8

opppss... i done it by integration, haha my bad
sorry, u are right
first derivative 2e^(2x+1)
second 4e^(2x+1) = (2)^2e^(2x+1)
third 8e^(2x+1) = (2)^3e^(2x+1)
....
and so on
we'll get the generalize for derivative of f(x) :
f^(n)(x) = (2)^n * e^(2x+1)

Answer 9

perfect!!!

Answer 10

how did you do the generalizing?

Answer 11

thanks for medal, and for this time i have to give u medal too :)

Answer 12

haha :) tnx

Answer 13

i see i see it now, i was trying 2n, but it was 2^n

Answer 14

look, the rithme the numbers 2,4,8,16,32,64,... so on
it can be 2, 2^2, 2^3, 2^4, 2^5, 2^6, ..., till 2^n

Answer 15

got it!

Answer 16

yeah, u are right