# How do you use the limit definition of the derivative to find the derivative of #f(x)=sqrt(x)-2x+1#?

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To find the derivative of ( f(x) = \sqrt{x} - 2x + 1 ) using the limit definition of the derivative, follow these steps:

- Start with the function ( f(x) ).
- Write down the limit definition of the derivative: ( f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} ).
- Substitute the function ( f(x) = \sqrt{x} - 2x + 1 ) into the limit definition.
- Simplify the expression.
- Take the limit as ( h ) approaches 0.
- Calculate the derivative ( f'(x) ).

This process will yield the derivative of the function ( f(x) = \sqrt{x} - 2x + 1 ).

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