# How do you differentiate #f(x)=1/(x^3-1)*x^2*cosx# using the product rule?

Using the product rule

putting thins together we get

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To differentiate ( f(x) = \frac{x^2 \cos(x)}{x^3 - 1} ) using the product rule:

- Let ( u(x) = x^2 ) and ( v(x) = \cos(x) )
- Find ( u'(x) ) and ( v'(x) )
- Apply the product rule:

( f'(x) = u'(x)v(x) + u(x)v'(x) ) - Substitute the values into the formula:

( f'(x) = (2x)(\cos(x)) + (x^2)(-\sin(x)) ) - Simplify the expression:

( f'(x) = 2x\cos(x) - x^2\sin(x) )

Therefore, the derivative of ( f(x) = \frac{x^2 \cos(x)}{x^3 - 1} ) using the product rule is ( f'(x) = 2x\cos(x) - x^2\sin(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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