# How do you differentiate #f(x)=(5e^x+tanx)(x^2-2x)# using the product rule?

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To differentiate ( f(x) = (5e^x + \tan(x))(x^2 - 2x) ) using the product rule, first identify the functions ( u(x) = 5e^x + \tan(x) ) and ( v(x) = x^2 - 2x ). Then apply the product rule formula:

[ f'(x) = u'(x)v(x) + u(x)v'(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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