# How do you differentiate #f(x)=(cos^3x)/sinx# using the quotient rule?

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To differentiate ( f(x) = \frac{\cos^3(x)}{\sin(x)} ) using the quotient rule, follow these steps:

- Identify ( u ) and ( v ) in the function ( f(x) = \frac{u}{v} ).
- Apply the quotient rule formula: ( f'(x) = \frac{u'v - uv'}{v^2} ).
- Differentiate ( u = \cos^3(x) ) with respect to ( x ) to find ( u' ).
- Differentiate ( v = \sin(x) ) with respect to ( x ) to find ( v' ).
- Substitute ( u' ), ( v' ), ( u ), and ( v ) into the quotient rule formula.
- Simplify the expression to obtain the derivative of ( f(x) ).

Following these steps will enable you to differentiate ( f(x) = \frac{\cos^3(x)}{\sin(x)} ) using the quotient rule.

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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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