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Lesson 5, Topic 6
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# Product Rule

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If y = uv , where u and v are functions of x,

then

$$\normalsize \frac{dy}{dx} = \scriptsize u \normalsize \frac{dv}{dx} + \scriptsize v \normalsize \frac{du}{dx}$$

Example: Differentiate $$\scriptsize (3x -2)(x^2 + 3)$$ with respect to x

let u = (3x – 2) and v = x2 + 3

$$\frac{du}{dx} \scriptsize = 3$$

$$\frac{dv}{dx} \scriptsize = 2x$$

$$\normalsize \frac{dy}{dx} = \scriptsize u \normalsize \frac{dv}{dx} \times \scriptsize v \normalsize \frac{du}{dx}$$

$$\frac{dy}{dx} = \scriptsize (3x \; – \; 2) (2x) + (x^2 + 3) (3)$$

$$\frac{dy}{dx} = \scriptsize 6x^2 -4x + 3x^2 + 9$$

=$$\frac{dy}{dx} = \scriptsize 9x^2 – 4x + 9$$

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