Porisma

Worked solution

Use the requested product rule

Differentiate (3x2+1)(2x+7)(3x^2+1)(2x+7) with respect to xx using the product rule.

CJC · O Level revision · Example 25

Answer

2(9x2+21x+1)2(9x^2+21x+1).

Compare your reasoning

Differentiate each factor once

ddx[(3x2+1)(2x+7)]=(3x2+1)ddx(2x+7)+(2x+7)ddx(3x2+1)\begin{aligned}&\frac{d}{dx}[(3x^2+1)(2x+7)]\\ & =(3x^2+1)\frac{d}{dx}(2x+7)\\ &{}+(2x+7)\frac{d}{dx}(3x^2+1)\end{aligned}

Retain the requested product-rule method rather than replacing it with only an expanded polynomial calculation.

Substitute the derivatives and collect

(3x2+1)(2)+(2x+7)(6x)=2[3x2+1+3x(2x+7)]=2(9x2+21x+1)\begin{aligned}&(3x^2+1)(2)\\ &{}+(2x+7)(6x)\\ & =2[3x^2+1+3x(2x+7)]\\ & =2(9x^2+21x+1)\end{aligned}

Both printed simplification stages are retained.

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