# How do you differentiate #(x^3 - 9x)/(x^2-7x+12)#?

First, let us simplify the expression

Now differentiate using the quotient rule.

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To differentiate the function ( \frac{{x^3 - 9x}}{{x^2 - 7x + 12}} ), you can use the quotient rule. The quotient rule states that if you have a function in the form ( \frac{{f(x)}}{{g(x)}} ), the derivative is given by ( \frac{{f'(x)g(x) - f(x)g'(x)}}{{[g(x)]^2}} ). Applying this rule to the given function, the derivative is ( \frac{{3x^2(x^2 - 7x + 12) - (x^3 - 9x)(2x - 7)}}{{(x^2 - 7x + 12)^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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