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

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

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

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

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derivative of

x^{2} (3 - x)

6 x - 3 x^{2}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = 3 - x

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

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

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

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

Simplify

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

= 6 x - 3 x^{2}

c y^{- 6}

x \to 1 lim (x^{3} - 2 x^{2} + x - 3)

x^{6}

\frac{d}{d x} (\frac{90}{x})

x \to \infty lim (x^{2} + 1)

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