# How do you differentiate #f(x)= (4x^2-1) *ln x# using the product rule?

The product Rule:

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To differentiate ( f(x) = (4x^2 - 1) \cdot \ln x ) using the product rule, apply the formula:

[ (uv)' = u'v + uv' ]

where ( u = 4x^2 - 1 ) and ( v = \ln x ). Then, differentiate each term:

[ u' = 8x ] [ v' = \frac{1}{x} ]

Finally, substitute these derivatives into the product rule formula:

[ f'(x) = (4x^2 - 1) \cdot \frac{1}{x} + (8x) \cdot \ln 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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