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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.

 Aug 3, 2017
 #1
avatar+27578 
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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.

.

 Aug 3, 2017
 #2
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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 ?

 Aug 3, 2017
 #3
avatar+27578 
+1

"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! + ...

 

.

 Aug 3, 2017

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