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

The derivative of (1-x^3-3x(1-x)^2) is -12x^2+18x-6

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

The first derivative of (1-x^3-3x(1-x)^2) is -12x^2+18x-6

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

- 12 x^{2} + 18 x - 6

Solution steps

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

Simplify

(1 - x)^{3} - 3 x (1 - x)^{2} : - 4 x^{3} + 9 x^{2} - 6 x + 1

= \frac{d}{d x} (- 4 x^{3} + 9 x^{2} - 6 x + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (9 x^{2}) - \frac{d}{d x} (6 x) + \frac{d}{d x} (1)

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (9 x^{2}) = 18 x

\frac{d}{d x} (6 x) = 6

\frac{d}{d x} (1) = 0

= - 12 x^{2} + 18 x - 6 + 0

Simplify

= - 12 x^{2} + 18 x - 6

What is the derivative of (1-x^3-3x(1-x)^2) ?
The derivative of (1-x^3-3x(1-x)^2) is -12x^2+18x-6
What is the first derivative of (1-x^3-3x(1-x)^2) ?
The first derivative of (1-x^3-3x(1-x)^2) is -12x^2+18x-6