How do you differentiate #f(x)=(x+1)(x+2)(x+3)# using the product rule?
You consider two of the factors as one, doing somewhat of a chain rule here.
In general terms, we can state that a product rule for three terms can be depicted as follows:
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To differentiate ( f(x) = (x + 1)(x + 2)(x + 3) ) using the product rule, follow these steps:

Identify the functions ( u ) and ( v ). ( u = (x + 1)(x + 2) ) ( v = x + 3 )

Differentiate ( u ) and ( v ) separately. ( u' = (2x + 3) ) ( v' = 1 )

Apply the product rule: ( (uv)' = u'v + uv' ). ( f'(x) = (2x + 3)(x + 3) + (x + 1)(x + 2)(1) )

Simplify the expression. ( f'(x) = (2x^2 + 9x + 9) + (x^2 + 3x + 2) )

Combine like terms. ( f'(x) = 3x^2 + 12x + 11 )
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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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