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

Answer 1

William Abdalla

until the admins can merge them, here is the same question with answer: https://tutor.hix.ai

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Answer 2

Axel Alvarez

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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Answer from HIX Tutor

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.