# How do you differentiate #f(x)=x^6/(x-6)# using the quotient rule?

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To differentiate the function ( f(x) = \frac{x^6}{x - 6} ) using the quotient rule, follow these steps:

- Identify ( u(x) ) as the numerator ( x^6 ) and ( v(x) ) as the denominator ( x - 6 ).
- Apply the quotient rule: ( f'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} ).
- Find the derivatives of ( u(x) ) and ( v(x) ).
- Substitute the values into the quotient rule formula.
- Simplify the expression to obtain the derivative ( f'(x) ).

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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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