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.


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