# How do you calculator the derivative for #(2x-5)/(x^(2)-4)#?

so we get:

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To find the derivative of the function ( f(x) = \frac{2x - 5}{x^2 - 4} ), you can use the quotient rule, which states that if ( f(x) = \frac{g(x)}{h(x)} ), then ( f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2} ). Applying the quotient rule to the given function:

[ f'(x) = \frac{(2)(x^2 - 4) - (2x - 5)(2x)}{(x^2 - 4)^2} ]

[ f'(x) = \frac{2x^2 - 8 - 4x^2 + 10x}{(x^2 - 4)^2} ]

[ f'(x) = \frac{-2x^2 + 10x - 8}{(x^2 - 4)^2} ]

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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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