According to which rules of differentiation do you think that ?
I'm not sure what I'm doing wrong here...
S(t) = 20,000(1 + e^{-0.5t})
Find the rate of change when t=1
S'(t) = 20,000(1 + e^{-0.5t}) d/dx(-0.5t)
= -10,000(1+e^{-0.5t})
S'(1) = -10,000(1+ e^{-0.5[1]})
= -10,000(1 + (0.606530659)
= -10,000(1.606530659)
= -16,065
Apparently I should be getting -6,065 instead. I realize that this has something to do with the fact that the '1 + ...." is still in the expression, when it shouldn't be, but I'm not sure how I should be getting rid of it..
I'm going by the chain rule, according to my text-book. From what I understand by my textbook, if f(x) in is differentiable, then the derivative of .
I realize I'm going wrong here, and it's a bit of a pain because I'm doing this via distance education, which has been lacking at the best of times. I'd be stuffed without this forum.
Hmm, I was aware of it, I Remember that rule from when I was doing derivatives without an exponential. I didn't think of it during this question however.
So, I'm guessing it should be something more like this..?
Due to S'(t) removing the constant value from the equation?
What I can suggest is rewriting the derivative one step at a time. At each step do a single transformation and be sure to identify which of the rules given here you are using.
I still don't understand how you obtained the right-hand side. Also, the notation is incorrect. Even does not mean the derivative of 0.5t.
First, it should be f(t), not f(x). I assume that f(t) denotes the exponent. Second, S'(t) = S(t) * f '(t) is false because it is not an instance of the chain rule. The correct instance would be R(f(t))' = R'(f(t)) f'(t) where R(x) = 20,000(1 + e^x). Also, it may be easier to factor 20,000 through first.