Find the derivative of the function by the limit process.

Name: Find the derivative of the function by the limit process.
Brand: Quizplus
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Question

Find the derivative of the function  by the limit process.

Quizplus · Accepted Answer

Using the limit process, we have

f'(x) = lim(h->0)[(11e^(x+h) − 11e^x)/h] 
= lim(h->0)[11e^x(e^h − 1)/h] 
= 11e^x lim(h->0)[(e^h − 1)/h]

We recognize the limit inside the parentheses as the derivative of e^x at x=0, so it is equal to 1. Therefore,

f'(x) = 11e^x

which matches choice C.

Find the Derivative of the Function by the Limit