Re: Where am I going wrong?

According to which rules of differentiation do you think that $\displaystyle (1+e^{f(t)})'=(1+e^{f(t)})f'(t)$?

Re: Where am I going wrong?

Quote:

Originally Posted by

**emakarov** According to which rules of differentiation do you think that $\displaystyle (1+e^{f(t)})'=(1+e^{f(t)})f'(t)$?

I'm going by the chain rule, according to my text-book. From what I understand by my textbook, if f(x) in $\displaystyle e^f(x)$ is differentiable, then the derivative of $\displaystyle e^f(x) = e^f(x) * dx f(x)$.

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.

Re: Where am I going wrong?

You are right about $\displaystyle (e^{f(t)})'$ (up to some typos). What about $\displaystyle \left(1+e^{f(t)}\right)'$? Do you know that $\displaystyle (g(t) + h(t))' = g'(t) + h'(t)$ and $\displaystyle c' = 0$ for a constant c?

Re: Where am I going wrong?

Quote:

Originally Posted by

**emakarov** You are right about $\displaystyle (e^{f(t)})'$ (up to some typos). What about $\displaystyle \left(1+e^{f(t)}\right)'$? Do you know that $\displaystyle (g(t) + h(t))' = g'(t) + h'(t)$ and $\displaystyle c' = 0$ for a constant c?

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..?

$\displaystyle S'(t) = 20,000(1 + e^{-0.5t}) * dx (0.5t)

= -10,000(e^{-.5t})$

Due to S'(t) removing the constant value from the equation?

Re: Where am I going wrong?

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.

Quote:

$\displaystyle S'(t) = 20,000(1 + e^{-0.5t}) * dx (0.5t)$

I still don't understand how you obtained the right-hand side. Also, the notation $\displaystyle dx (0.5t)$ is incorrect. Even $\displaystyle dt(0.5t)$ does not mean the derivative of 0.5t.

Re: Where am I going wrong?

Quote:

Originally Posted by

**emakarov** 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 $\displaystyle dx (0.5t)$ is incorrect. Even $\displaystyle dt(0.5t)$ does not mean the derivative of 0.5t.

I obtained the right side because I thought that S'(t) = S(t) * f '(x).

If f(x) = -0.5t, then f '(x) = -0.5 ?

Re: Where am I going wrong?

Quote:

Originally Posted by

**astuart** I obtained the right side because I thought that S'(t) = S(t) * f '(x).

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.