ok i just need to know if i have the right derivative for this function
e^(2t)
would the correct derivative be
2e^(2t)?
thanks
mathlete
It's just using the chain rule:
We know that:
$\displaystyle \frac{dy}{dx}[e^t] = e^t$
Say u equals some function of t (that is differentiable, of course):
$\displaystyle u = f(t)$
Then:
$\displaystyle \frac{dy}{dx}[e^u] = u'e^u$
$\displaystyle \frac{dy}{dx}[e^{2t}] = [2t]'e^{2t}$
$\displaystyle [2t]'e^{2t} = 2e^{2t}$
So yes, you are correct.