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

The derivative of x(1-x^2) is 3x^2-4x+1

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

The first derivative of x(1-x^2) is 3x^2-4x+1

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

3 x^{2} - 4 x + 1

Solution steps

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

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

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

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

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

Simplify

1 \cdot (1 - x)^{2} + (- 2 (1 - x)) x : 3 x^{2} - 4 x + 1

= 3 x^{2} - 4 x + 1

What is the derivative of x(1-x^2) ?
The derivative of x(1-x^2) is 3x^2-4x+1
What is the first derivative of x(1-x^2) ?
The first derivative of x(1-x^2) is 3x^2-4x+1