Can someone show me how this is done: Differentiation of e^x

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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

Alan · Answer 1 · 2017-08-03T08:01:42

Here is the rule and its derivation:

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

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Guest · Answer 2 · 2017-08-03T09:14:07

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 ?

Alan · Answer 3 · 2017-08-03T10:55:36

"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 + x²/2! + ...

Or sometimes just directly as 1 + x + x²/2! + ...

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