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

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

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

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

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

2 (1 - 2 x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = 1 - x

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

\frac{d x}{d x} = 1

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

= 2 (1 \cdot (1 - x) + (- 1) x)

Simplify

2 (1 \cdot (1 - x) + (- 1) x) : 2 (1 - 2 x)

= 2 (1 - 2 x)

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