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# 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. e4x

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
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#1
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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
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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
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"Do you not need to know the derivative of e^x in order to write down its series expansion ?"

No.

ex is often defined as limitn→infinity(1+x/n)→ limitn→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! + ...

.

Alan  Aug 3, 2017

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