Why is e^3x = 3e^3x

[high hawk]

the video didnt say, surely it e^3x = e^3x

[hardy fox]

No it's e^3x = 3e^3x. Bcz think of e^3x as a composite function so its derivative will be the product of f'(g(x) )g'(x).

[high hawk]

bruh

i dnt understand

[whole surge]

3e^(3x) is the derivative of e^3x

[alpine schooner]

If you have e^f(x), the derivative is e^[f(x)]*ln(e) times d/dx[f(x)]. So for e^3x, you have e^3x times 3 = 3e^3x

[versed pewter]

A composite function is of the form f(g(x)), which in this case f is e^x while g is 3x

[high hawk]

Ok andd im not sure that will help me

[versed pewter]

Do you remember the chain rule formula?

[high hawk]

oh im not on that part yet

its the topic after this i think

[versed pewter]

Yea that's needed to understand the derivative you're having trouble with

[high hawk]

ah ok

[versed pewter]

The chain rule applies for composite functions

[high hawk]

then i will learn it and come back

[versed pewter]

Sure

[high hawk]

but in this context

if we replaced x with 3x, is the expansion still valid?

as in if it was y = e^3x

or is this expansion only valid for e^x

https://youtu.be/uVJFfPuYMXA?si=FLXFnpthletyPKeo&t=28

[versed pewter]

It's valid for all kinds of inputs

Be it x, 3x, x^2 or whatever else