What is the derivative of x^2(6-x) ?

The derivative of x^2(6-x) is 12x-3x^2

What is the first derivative of x^2(6-x) ?

The first derivative of x^2(6-x) is 12x-3x^2

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\frac{d}{d x} (x^{2} (6 - x))

12 x - 3 x^{2}

Solution steps

\frac{d}{d x} (x^{2} (6 - x))

Apply the Product Rule:

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

f = x^{2}, g = 6 - x

= \frac{d}{d x} (x^{2}) (6 - x) + \frac{d}{d x} (6 - x) x^{2}

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

\frac{d}{d x} (6 - x) = - 1

= 2 x (6 - x) + (- 1) x^{2}

Simplify

2 x (6 - x) + (- 1) x^{2} : 12 x - 3 x^{2}

= 12 x - 3 x^{2}

x y^{^{'}} - 2 y = x^{2} - x - 2

\frac{d}{d y} (5 y)

\frac{\partial}{\partial t} (arctan (t))

x \to + 2 lim (7 - 3 x^{2} - x^{3})

y^{^{'}} = x e^{y - x^{2}}

What is the derivative of x^2(6-x) ?
The derivative of x^2(6-x) is 12x-3x^2
What is the first derivative of x^2(6-x) ?
The first derivative of x^2(6-x) is 12x-3x^2