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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int_{1}^{3} (9^{x} - 7^{x}) d x

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

y^{^{'}} = 7 y

\frac{d}{d x} ((2 x + 1)^{5} + 10 x (2 x + 1)^{4})

\frac{\partial}{\partial s} (2 s^{2} + t^{2})

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