Question

Help with derivative of exponential functions please!!

Answer 1

where does the y come from?

Answer 2

what did you get for y'?

Answer 3

y'= 5/2 [1/5e^(x/5) - 1/5e^(-1/5)]

Answer 4

ok that is very good

Answer 5

so what happens if you find derivative again

Answer 6

y''= 1/10 [e^(1/5) + e^(/1/5)]

Answer 7

\[y''=\frac{1}{25} \cdot \frac{5}{2}(e^\frac{x}{5}+e^{-\frac{x}{5}}) \]
or this right?

Answer 8

yep

Answer 9

so isn't y=5/2(exp(x/5)+exp(-x/5))?

Answer 10

remember \[y=\frac{5}{2}(e^\frac{x}{5}+e^\frac{-x}{5}) ?\]

Answer 11

yes

Answer 12

ok so replace it with y
then you have y''=y/25

Answer 13

ohhh wow, i see. i didn't notice that. thank you so much :)

Answer 14

yep yep
lol
usually when you find y'' you can replace something with y