derivative of x^2(240-x/3) — step-by-step solution

Let's perform the differentiation:

\frac{d}{d x} (x^{2} \cdot (240 - \frac{x}{3}))

We differentiate

U1

x^{2}

and

V2

240 - \frac{x}{3}

using:

\frac{d}{d x} (U1 \cdot V2) = \frac{d}{d x} (U1) \cdot V2 + U1 \cdot \frac{d}{d x} (V2)

Let's perform the differentiation

U1

\frac{d}{d x} (x^{2})

2 x

Let's differentiate

V2

\frac{d}{d x} (240 - \frac{x}{3})

0 + \frac{d}{d x} (- \frac{x}{3})

- \frac{1}{3}

Let's evaluate the resulting derivative (

U1 \cdot V2

)':

2 x \cdot (240 - \frac{x}{3}) + x^{2} \cdot (- \frac{1}{3})

2 x \cdot (240 - \frac{x}{3}) - \frac{x^{2}}{3}

(480 x + 2 x \cdot (- \frac{x}{3})) - \frac{x^{2}}{3}

480 x - \frac{2 x^{2}}{3} - \frac{x^{2}}{3}

480 x - x^{2}

▶Derivative:

x \cdot (480 - x)