# How do you use the product rule to differentiate #g(x)=(x^2+1)(x^2-2x)#?

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To use the product rule to differentiate ( g(x) = (x^2 + 1)(x^2 - 2x) ), follow these steps:

- Identify the functions ( f(x) = x^2 + 1 ) and ( h(x) = x^2 - 2x ).
- Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function.
- Calculate the derivatives of ( f(x) ) and ( h(x) ).
- Substitute the derivatives and the original functions into the product rule formula.
- Simplify the expression to get the derivative of ( g(x) ).

Using the product rule, the derivative of ( g(x) ) is: [ g'(x) = (2x)(x^2 - 2x) + (x^2 + 1)(2x - 2) ]

After simplifying, the final result is: [ g'(x) = 2x^3 - 4x^2 + 2x - 2 ]

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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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