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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x - 1)^{3}

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

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

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

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

Simplify

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

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