What is the derivative of e^(2x)

I am confused because the derivative e^x is e^x.
But they say you need to use the chain rule.

Which is f'(g(x))*g'(x).
I have used that on exponents but in this I just get, 2x * e^(2x-1) *e
Which is not the answer =/

Question

What is the derivative of e^(2x)

I am confused because the derivative e^x is e^x.
But they say you need to use the chain rule.

Which is f'(g(x))*g'(x).
I have used that on exponents but in this I just get, 2x * e^(2x-1) *e
Which is not the answer =/

anonymous · Answer

2e^(2x)

amistre64 · Answer

$$y=e^{2x}$$
$$ln(y)=2x$$
$$y'/y = 2$$
$$y'=2y;\ but\ y=e^{2x}$$

$$y' = 2e^{2x}$$

anonymous · Answer

So I just have to use logs, to differentiate it.

shayaan_mustafa · Answer

@amistre64 
will you kindly elaborate elaborate your 3rd step i.e. y'/y=2
how did you get this? please.

s3a · Answer

(Chain) rule:
d/dx e^[f(x)] = df(x)/dx * e^[f(x)]

Examples:

1) d/dx e^x = dx/dx * e^x = 1 * e^x = e^x

2) d/dx e^(2x) = d(2x)/dx * e^(2x) = 2 * e^(2x)

s3a · Answer

Shayaan_Mustafa, if you treat y as a function (and not just a regular variable) then you take the derivative of y as if it's just a regular variable and you turn the y into a y'.

s3a · Answer

Example if y = y(x),

d/dx (y^2) = 2y * y'

anonymous · Answer

1) d/dx e^x = dx/dx * e^x = 1 * e^x = e^x

why does e^x = 1?

anonymous · Answer

o wait

s3a · Answer

d(x)/dx = 1

s3a · Answer

in this case f(x) = x.

s3a · Answer

This being e^x.

anonymous · Answer

ok , I kinda get it. So all I have to do is use the chain rule, why did he use the ln rule above?

s3a · Answer

He was proving it.

s3a · Answer

In other words, the very first time mathematicians had to do this, they had to justify why what I said works.

s3a · Answer

I think.

s3a · Answer

If someone can confirm, that'd be great (for me).

anonymous · Answer

ok lol =P

s3a · Answer

:)

anonymous · Answer

Thanks for the help everyone, I'm a little closer to understanding it.