What is the derivative of #(x-1)(x^2+2)^3#?
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To find the derivative of ( (x-1)(x^2+2)^3 ):
- Identify the functions being multiplied: ( f(x) = x - 1 ) and ( g(x) = (x^2 + 2)^3 ).
- Apply the product rule: ( (fg)'(x) = f'(x)g(x) + f(x)g'(x) ).
- Find the derivatives of ( f(x) ) and ( g(x) ):
- ( f'(x) = 1 )
- ( g'(x) = 3(x^2 + 2)^2 \cdot (2x) ).
- Substitute the derivatives and functions into the product rule formula.
- Simplify the expression.
- Combine like terms if necessary to get the final result.
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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.
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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