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(1) Find the derivative of f(x)=\frac{5}{3x+5} using the limit definition of derivative. (2) Find...

Question:

(1) Find the derivative of {eq}f(x)=\frac{5}{3x+5} {/eq} using the limit definition of derivative. (2) Find the derivative of {eq}f(x)=\sqrt{3x+5} {/eq} using the limit definition of derivative.

Differentiation by the Limit Derivative Method:

{eq}\displaystyle \text{We can find any derivative by using the limit definition of a derivative.}\\[10pt] \text{This is the process of finding the derivative of function f(x) by using the following definition}\\[10pt] f'(x)=\lim_{h\to0} \frac{f(x+h)-f(x)}{h}\\ {/eq}

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Answer and Explanation:

we can apply the limit definition of a derivative to differentiate this function:

{eq}\displaystyle{\text{Let}f(x)=\frac{5}{3x+5}\\[10pt] \text{Then...

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Using Limits to Calculate the Derivative

from Math 104: Calculus

Chapter 8 / Lesson 1
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