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Differentiation: Product Rule

Q:  Find the derivative of (x² – 5x + 2)*(x – 2/x)

A:  First, I am going to rewrite the problem:

(x² – 5x + 2)*(x – 2/x) = (x² – 5x + 2)*(x – 2x-1)

Now, we are going to apply the product rule.  The product rule tells us how to take the derivative of a function times another function: f*g

The product rule says that the derivative of f*g is f ‘ * g + g ‘ * f

f = x² – 5x + 2        g = x – 2x-1

f ‘ = 2x – 5              g’ = 1 + 2x-2

So, plug the following in to f ‘ * g + g ‘ * f to get the answer:

(2x – 5)(x – 2x-1) + (1 + 2x-2)(x² – 5x + 2)

You could also reverse the order:

(1 + 2x-2)(x² – 5x + 2) + (2x – 5)(x – 2x-1)

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