What is the derivative of x^2(120-x) ?

The derivative of x^2(120-x) is 240x-3x^2

What is the first derivative of x^2(120-x) ?

The first derivative of x^2(120-x) is 240x-3x^2

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derivative of

x^{2} (120 - x)

240 x - 3 x^{2}

Solution steps

\frac{d}{d x} (x^{2} (120 - x))

Apply the Product Rule:

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

f = x^{2}, g = 120 - x

= \frac{d}{d x} (x^{2}) (120 - x) + \frac{d}{d x} (120 - x) x^{2}

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

\frac{d}{d x} (120 - x) = - 1

= 2 x (120 - x) + (- 1) x^{2}

Simplify

2 x (120 - x) + (- 1) x^{2} : 240 x - 3 x^{2}

= 240 x - 3 x^{2}

\int 10 sec^{2} (5 x) tan (5 x) d x

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\frac{d Q}{d t} = 14.5 - \frac{7 Q}{800 - 2 t}

What is the derivative of x^2(120-x) ?
The derivative of x^2(120-x) is 240x-3x^2
What is the first derivative of x^2(120-x) ?
The first derivative of x^2(120-x) is 240x-3x^2