Math Help - derivative

1. derivative

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

2. It's just using the chain rule:

We know that:

$\frac{dy}{dx}[e^t] = e^t$

Say u equals some function of t (that is differentiable, of course):

$u = f(t)$

Then:

$\frac{dy}{dx}[e^u] = u'e^u$

$\frac{dy}{dx}[e^{2t}] = [2t]'e^{2t}$

$[2t]'e^{2t} = 2e^{2t}$

So yes, you are correct.

3. sample equation

sample:

y=e^5x
y= (5x)'(e^(5x))
y'= 5 (e^(5x))

solution:

y = e^(2t)

y = (2t)'(e^2t)

y = 2e^2t

4. That's correct. You use the chain rule.

5. I love the quick, detailed, and numerous responses that MHF provides!