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

Applying the quotient rule, we have the derivative equalling

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The derivative can be written:

This can clearly be differentiated using the quotient rule, but it is also possible to rewrite the expression before differentiating.

This result can be written in other forms:

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To find the derivative of ((2x^2 + x - 3)/x), you can use the quotient rule of differentiation. The quotient rule states that for functions (u(x)) and (v(x)), the derivative of their quotient (\frac{u(x)}{v(x)}) is given by:

[\frac{d}{dx}\left(\frac{u(x)}{v(x)}\right) = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}]

Applying the quotient rule to the given function:

[u(x) = 2x^2 + x - 3]

[u'(x) = 4x + 1]

[v(x) = x]

[v'(x) = 1]

Now, substitute these values into the quotient rule formula:

[\frac{d}{dx}\left(\frac{2x^2 + x - 3}{x}\right) = \frac{(4x + 1)(x) - (2x^2 + x - 3)(1)}{(x)^2}]

Simplify the expression:

[= \frac{4x^2 + x - (2x^2 + x - 3)}{x^2}]

[= \frac{4x^2 + x - 2x^2 - x + 3}{x^2}]

[= \frac{2x^2 + 3}{x^2}]

Therefore, the derivative of ((2x^2 + x - 3)/x) is (\frac{2x^2 + 3}{x^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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