# Differentation Problem (involves product rule)

#### Cod

Here's the equation:

F(x) = (x-1)(x-2)(x-3)

I know how to diff. using the product rule when you only have 2 equations, but not 3.I looked at the examples in my book and none of them show how you would work out this sort of problem. So if someone could give me the basic overview of how to differentiate a problem like this, I'd greatly appreciate it.

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#### Cod

Just wondering something...

Could I change the equation to read like this before diff. it:

F(x) = (x-1)(x^2-5x+6) ???

Then I could just use the product rule from there.

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#### himanshu121

consider u,v,w as a function of x

then $$\frac{d}{dx}uvw = uv \frac{d}{dx}w + vw\frac{d}{dx}u + uw\frac{d}{dx}v$$

#### ShawnD

Just expand it then differentiate. According to Maple, you get the same answer.

Here is when you differentiate 3 terms

> R3 := diff((x-1)*(x-2)*(x-3),x);

R3 := (x - 2) (x - 3) + (x - 1) (x - 3) + (x - 1) (x - 2)

> R4 := expand(R3);
R4 := 3 x^2 - 12 x + 11

Here is when you expand it then differentiate it

R1 := expand((x-1)*(x-2)*(x-3));
R1 := x^3 - 6 x^2 + 11 x - 6

> R2 := diff(R1,x);
R2 := 3 x^2 - 12 x + 11

You end with the same answer. Just expand it; it's much easier.