How do you differentiate #f(x) = 1/(x^34x)# using the quotient rule?
Quotient rule states that for a function
To be honest, I'd better use chain rule, here, but let's do as you asked.
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To differentiate ( f(x) = \frac{1}{x^3  4x} ) using the quotient rule:

Identify ( u ) and ( v ): ( u = 1 ) ( v = x^3  4x )

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

Find the derivatives of ( u ) and ( v ): ( u' = 0 ) ( v' = 3x^2  4 )

Substitute into the quotient rule formula: ( f'(x) = \frac{(0)(x^3  4x)  (1)(3x^2  4)}{(x^3  4x)^2} )

Simplify: ( f'(x) = \frac{3x^2 + 4}{(x^3  4x)^2} )
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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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