How do you find the derivative of $e^x$ using the limit definition?

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Answer 1 · 2016-08-01T09:06:02

See the Explanation.

We will use the following Standard Form of Limit :

$lim_(hrarr0) (e^h -1)/h=1$ .

Let $f(x)=e^x rArr f(x+h)=e^(x+h)$

Now, $f'(x)=lim_(hrarr0) {f(x+h)-f(x)}/h$

$=lim_(hrarr0) {e^(x+h)-e^x}/h$

$=lim_(hrarr0) {e^x(e^h-1)}/h$

$=e^x{lim_(hrarr0) (e^h-1)/h}$

$=e^x.1$

$e^x$ .

How do you find the derivative of e^x e^x using the limit definition?