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#.