# Calc2.30

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Find the derivative of $f(x)\,$ with respect to $x\,$: $f(x)=(x)(x+7)(x-12)\,$

There are many ways to do this problem but here we will use it to illustrate the product rule on three terms.

$(abc)'=a'(bc)+b'(ac)+c'(ab)\,$

$f'(x)={\frac {d(x)}{dx}}(x+7)(x-12)+{\frac {d(x+7)}{dx}}(x)(x-12)+{\frac {d(x-12)}{dx}}(x)(x+7)\,$

$f'(x)=(x+7)(x-12)+(x)(x-12)+(x)(x+7)\,$

Another way you can try this is to use the product rule for two terms and take $a=x\,$ and $b=(x+7)(x-12)\,$. Then, when computing the derivative of $b\,$ you'll have to use the product rule again but the answer will be the same either way.

A third way to do the problem is to multiply the polynomial out and then take the derivative using the product rule.