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

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

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

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

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derivative of

x \cdot (1 - x)

1 - 2 x

Solution steps

\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

= \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

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

Simplify

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

= 1 - 2 x

\frac{\partial}{\partial y} (sin (x y))

\int (a + x)^{2} d x

\frac{d}{d x} (\frac{( x ^{2} - 1 ) ^{3}}{4})

n = 0 \sum \infty \frac{e ^{n}}{n ^{n}}

\frac{\partial}{\partial y} (sin (x^{2}) - y)

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