Please show me step by step of how to differentiate these two questions, as well as the rule you used.
Im having trouble differentiationing e. If you guys could answer these question, i can probably understand.
Here is the rule and its derivation:
You should now be able to do your questions by choosing an appropriate value for k.
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 ?
"Do you not need to know the derivative of e^x in order to write down its series expansion ?"
ex is often defined as limitn→infinity(1+x/n)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! + ...