Please show me step by step of how to differentiate these two questions, as well as the rule you used.

1. e^{4x}

2. exp(-2x)

3. 20(1-e^{-}^{2x})

Im having trouble differentiationing e. If you guys could answer these question, i can probably understand.

Thanks.

Guest Aug 3, 2017

#1**+1 **

Here is the rule and its derivation:

You should now be able to do your questions by choosing an appropriate value for k.

.

Alan
Aug 3, 2017

#2**0 **

Isn't that a circular argument ?

Do you not need to know the derivative of e^x in order to write down its series expansion ?

Guest Aug 3, 2017

#3**+1 **

"Do you not need to know the derivative of e^x in order to write down its series expansion ?"

No.

e^{x} is often defined as limit_{n→infinity}(1+x/n)^{n }→ limit_{n→infinity}(1 + n(x/n) + (1/2!)n(n-1)(x/n)^{2} + ...)

→ 1 + x + x^{2}/2! + ...

Or sometimes just directly as 1 + x + x^{2}/2! + ...

.

Alan
Aug 3, 2017