Question

the deriviative of e^2x

Answer 1

do you know the derivative of e^x ?

Answer 2

e^x

Answer 3

use u substitution

Answer 4

great, now just use the chain rule
do you know that?

Answer 5

how is that chain rule?

Answer 6

we haven't done it yet...
but this problem requires it

Answer 7

the chain rule is f'(gx)(gx)'

Answer 8

call \(2x=f(x)\)
now we can look at this like\[\large e^{f(x)}\]the derivative is then\[\large e^{f(x)}f'(x)\]

Answer 9

but i dont get how e^2x is a chain rule its not a function inside a fucntion

Answer 10

is it 2e^2x

Answer 11

yes it is.

Answer 12

the 2x is the function inside the function e^(whatever)

Answer 13

so e^-x would be -e^x

Answer 14

-e^-x*

Answer 15

\[y=a^{f(x)}\]
\[y'=a^{f(x)}*f'(x)*\ln a\]