What is the derivative of x^2(580-x/3) ?

The derivative of x^2(580-x/3) is 1160x-x^2

What is the first derivative of x^2(580-x/3) ?

The first derivative of x^2(580-x/3) is 1160x-x^2

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derivative of

x^{2} (580 - \frac{x}{3})

1160 x - x^{2}

Solution steps

\frac{d}{d x} (x^{2} (580 - \frac{x}{3}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = 580 - \frac{x}{3}

= \frac{d}{d x} (x^{2}) (580 - \frac{x}{3}) + \frac{d}{d x} (580 - \frac{x}{3}) x^{2}

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

\frac{d}{d x} (580 - \frac{x}{3}) = - \frac{1}{3}

= 2 x (580 - \frac{x}{3}) + (- \frac{1}{3}) x^{2}

Simplify

2 x (580 - \frac{x}{3}) + (- \frac{1}{3}) x^{2} : 1160 x - x^{2}

= 1160 x - x^{2}

What is the derivative of x^2(580-x/3) ?
The derivative of x^2(580-x/3) is 1160x-x^2
What is the first derivative of x^2(580-x/3) ?
The first derivative of x^2(580-x/3) is 1160x-x^2