How do you differentiate #f(x) =(1x)/(x^36)# using the quotient rule?
First, let's clarify what the quotient rule is:
The formula has a nice flow for memorization and can be read as "low d high minus high d low over low squared."
Using the rule of quotient,
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To differentiate ( f(x) = \frac{{1x}}{{x^3  6}} ) using the quotient rule, follow these steps:

Identify ( u ) and ( v ): ( u = 1  x ) ( v = x^3  6 )

Find ( u' ) and ( v' ) (the derivatives of ( u ) and ( v )): ( u' = 1 ) ( v' = 3x^2 )

Apply the quotient rule: ( f'(x) = \frac{{v \cdot u'  u \cdot v'}}{{v^2}} )

Substitute the values: ( f'(x) = \frac{{(x^3  6)(1)  (1  x)(3x^2)}}{{(x^3  6)^2}} )

Simplify the expression to get the derivative.
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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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