Question

what is the derivative of f(x)=e^-8x
please would someone be able to give me some pointers

Answer 1

\[\large f(x)=e^{-8x}\]


Hmm ok let's start here a sec.
Do you remember the derivative of e^x?

Answer 2

yes that is e^x

Answer 3

Yes very good.
This same rule will still apply.
We just need to take an extra step after we take it's derivative.

We apply the chain rule, multiplying by the derivative of the exponent.
We do this because the exponent is more than just simply "x".

Answer 4

\[\large f(x)=e^{-8x}\]
\[\large f'(x)=e^{-8x}\color{royalblue}{\left(-8x\right)'}\]

Understand what happened there?
The exponential term gave us the same thing back when we differentiated it.
But applying the chain rule, we'll have to multiply by the derivative of this blue term.

Answer 5

The prime on the blue term is to show we still need to take it's derivative.

Answer 6

What's the derivative of -8x?

Answer 7

is it -8?

Answer 8

Yes good :)

\[\large f'(x)=e^{-8x}\color{royalblue}{\left(-8x\right)'}\]
\[\large f'(x)=e^{-8x}\color{orangered}{\left(-8\right)}\]

Answer 9

Can you see the fancy code alright?
If you're using Internet Explorer it won't show up correctly.

Answer 10

not sure what you mean, i'm using chrome

Answer 11

Do you see the colors? The blue and orange text in the math that I typed earlier?

Answer 12

Oh ok nevermind then :)
Just making sure.
If you're using internet explorer it would have showed up like this instead:

\large f'(x)=e^{-8x}\color{orangered}{\left(-8\right)}

Which is a little confusing hehe

Answer 13

i see hehe, i can see the colours

Answer 14

\[\large f'(x)=-8e^{-8x}\]
Understand the process though?

The exponential will give us the same thing when we differentiate it.
We just need to make a copy of the exponent and multiply by it's derivative.

Answer 15

so would that be (-8) x (-8x)?

Answer 16

I'm a little confused by your question.
Maybe this picture can help illustrate :O
It's kinda just the same thing I was saying before, but with arrows lol.