Question 36

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Jambmaths question: 

The derivative of $(2x+1)(3x+1)$ is

Option A: 

$6x+1$

Option B: 

$12x+5$

Option C: 

$6x+5$

Option D: 

$12x+1$

Jamb Maths Solution: 

$\begin{align}  & \text{Method 1} \\ & \text{Let }y=(2x+1)(3x+1) \\ & y=6{{x}^{2}}+5x+1 \\ & \frac{dy}{dx}=\frac{d}{dx}\left( 6{{x}^{2}}+5x+1 \right)=12x+5 \\ & \text{Method 2} \\ & \text{Using the product rule} \\ & \frac{dy}{dx}=u\frac{dv}{dx}+v\frac{du}{dx} \\ & \frac{dy}{dx}=(2x+1)\frac{d}{dx}(3x+1)+(3x+1)\frac{d}{dx}(2x+1) \\ & \frac{dy}{dx}=(2x+1)(3)+(3x+1)(2)=12x+5 \\\end{align}$

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