What is the derivative of x^2(1-x) ?

The derivative of x^2(1-x) is 2x-3x^2

What is the first derivative of x^2(1-x) ?

The first derivative of x^2(1-x) is 2x-3x^2

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\frac{d}{d x} (x^{2} (1 - x))

2 x - 3 x^{2}

Solution steps

\frac{d}{d x} (x^{2} (1 - x))

Apply the Product Rule:

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

f = x^{2}, g = 1 - x

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

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

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

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

Simplify

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

= 2 x - 3 x^{2}

x \to 0 lim (\frac{ln ( 1 + 3 x )}{x})

\frac{d}{d y} (- \frac{y}{t ^{2} + y ^{2}})

\int - 17 sin^{4} (t) cos (t) d t

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

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

What is the derivative of x^2(1-x) ?
The derivative of x^2(1-x) is 2x-3x^2
What is the first derivative of x^2(1-x) ?
The first derivative of x^2(1-x) is 2x-3x^2