Question

How do I get the derivative of this function?

C=te^-4t.

Answer 1

Are you familiar with the product rule for differentiation?

Answer 2

ummm......d/dx(t) + d/dx(e^-4t)

?

Answer 3

simply derivative of e^x is same if it is w.r.t x
use product rule and the answer is e^-4t(1-4t)
:)

Answer 4

You have function C = f(t) = g(t)h(t). C' = f'(t) = g(t)h'(t) + g'(t)h(t)

Answer 5

With g(t) = t and h(t) = e^(-4t)

Answer 6

Ok what if C=Concentration and t=hours and I'm trying to find the change in concentration at time t

Answer 7

You're on the right track, but it starts with the product rule and the steps I outlined. Once you have the general derivative, you can get a specific value at a specific value for "t".

Answer 8

ok, so after i do the product rule amd I trying to solve for t? What happens to the c?

Answer 9

With the derivative, C becomes C' which is f ' (t)

Answer 10

c'=t(e^-4t)(-4) + 1(e^-4t)
?
then.... c'=-4t(e^-4t) ?

Answer 11

ln 4t=ln e^-4t
ln4t=-4t
ln4t/-4=t

or am I jus trying to find an equation for the rate of change?

Answer 12

c'=(1 - 4t)(e^-4t) You were very close. Now, you can use any particular "t".

Answer 13

I don't have a "t" it just says to find rate of change of concentration at time t

Answer 14

You just said " ... at time t" So, you either have a general "t" or a specific value for "t"

Answer 15

just a general "t" so would I leave it as c'=(1-4t)(e^-4t) ?

Answer 16

That's it! Sometimes no specific value is given, in which case you go with the general solution.

Answer 17

ok phew! Thank you so much!

Answer 18

Nice working with you. And good luck in all of your studies!