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How do you find the derivative of # (x^2-3x+5)/x#?

Answer 1

Emilia Aguilar

#1-5/x^2#

#frac{d}{dx}(frac{x^2 - 3x + 5}{x}) = frac{d}{dx}(x - 3 + 5/x)#

#= 1 - 0 - 5/x^2#

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Answer 2

Ezekiel Alexander

To find the derivative of ((x^2-3x+5)/x), you can use the quotient rule. The quotient rule states that if you have a function of the form (f(x) = \frac{g(x)}{h(x)}), then its derivative is given by:

[f'(x) = \frac{g'(x) \cdot h(x) - g(x) \cdot h'(x)}{(h(x))^2}]

So, for the function ((x^2-3x+5)/x), the derivative will be:

[f'(x) = \frac{(2x - 3) \cdot x - (x^2 - 3x + 5) \cdot 1}{x^2}]

Simplify this expression to find the derivative.

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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.