Question

please show the steps to find the first derivative of
P(t)=500/(1+e^(-t) )

Answer 1

check ur eqn again plz? there is no x in ur expression for f(x)

Answer 2

sorry its a population question so its P(t)

Answer 3

OK that makes more sense :)
u can rewrite it: P(t)=500*[1+e^(-t)]^-1
does it make the differentiation a lil easier?

Answer 4

oh I already got that step im not sure what to do after :/

(500)'(1+e^-t)+(500)[(1+e^-t)]
(1+e^-t)^-1+500[(-1(1+e^-t)^-2]
Im confused after that

Answer 5

OK substitute 1+e^-t = y ok?
so P(t)=500*y^-1 right?

Answer 6

then use dP/dt=dP/dy*dy/dt.....

Answer 7

and then solve it and resubstitute e back?

Answer 8

well yes but u need to use the eqn above too - u have seen it from ur book right?

Answer 9

right ya

Answer 10

so what u got? :)

Answer 11

for derivating (1+e^-t)^-1 I used the power rule

-1(1+e^-t)^-2 (-e^-t)
[(1+e^-t)(-e^-t)]^-2

Answer 12

u are jumping ahead, emily!!

remember dP/dt=dP/dy*dy/dt
P=500*y^-1
use Power rule to find what dP/dy is first plz?

Answer 13

ok so to derive P= 500*y^-1

P'(x)= -1(500)y^-2?

Answer 14

should be P'(y) but close enough :)
okay we get dP/dy; now we get to dy/dt...
y=1+e^-t
so what is dy/dt?

Answer 15

thats where im having difficulty :/ I dont know

Answer 16

do u know d(e^x)/dx=e^x?

Answer 17

oh i missed that lesson so i dnt quite understand it so is it like (1+e^-t)[(-1)(e^-t)]?

Answer 18

read up about d(e^x)/dx=e^x from the link below:
http://tutorial.math.lamar.edu/Classes/CalcI/DiffExpLogFcns.aspx

Answer 19

dy/dt=d(1)/dt+d(e^-t)/dt

= 0 + (-1)e^-t
=-e^-t

Answer 20

ok im trying my best :/

(1+e^-t)^-1+[500(-e^-t)^-2]

Answer 21

almost there, emily....i promise ok?

Answer 22

just refresh on what we have done:

dP/dt = dP/dy * dy/dt

dP/dy = -1(500)y^-2

dy/dt = -e^-t

with me so far?

Answer 23

ok lol um im giving up for now :/ but i do see that you have to mltiply them together

-1(500)y^-2(-e^-t)?

Answer 24

hahahaa why u giving up? dats ur ans right there, emily!!! :)

Answer 25

oh thank god

Answer 26

see its NOT that difficult :P