How do you differentiate #f(x)=(cosxx)/(sin3xx^2)# using the quotient rule?
As per the quotient rule,
Here,
so
and
so
These functions can be added to the quotient rule formula as follows:
which you could further develop to provide
Nevertheless, this is needless and more complicated.
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To differentiate ( f(x) = \frac{\cos(x)  x}{\sin(3x)  x^2} ) using the quotient rule:

Apply the quotient rule: [ f'(x) = \frac{( \sin(3x)  x^2 ) \cdot (\sin(x))  (\cos(x)  x) \cdot (3\cos(3x)  2x)}{(\sin(3x)  x^2)^2} ]

Simplify the expression.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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