# How do you find the derivative of #1/x^(1/2)# using [f(x+h)-f(x)]/h?

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To find the derivative of ( \frac{1}{x^{1/2}} ) using the difference quotient formula ( \frac{f(x+h)-f(x)}{h} ), follow these steps:

- Start with the function ( f(x) = \frac{1}{x^{1/2}} ).
- Replace ( f(x) ) with ( \frac{1}{x^{1/2}} ) in the difference quotient formula.
- Expand ( f(x+h) ) by substituting ( x+h ) into the function ( \frac{1}{x^{1/2}} ).
- Subtract ( f(x) ) from ( f(x+h) ).
- Simplify the expression obtained from step 4.
- Divide the result by ( h ).
- Simplify the expression further if possible.

After following these steps, you'll find the derivative of ( \frac{1}{x^{1/2}} ) using the difference quotient formula.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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