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

The derivative of (x^3-x(2x-x^2)) is -5x^4+8x^3+3x^2-4x

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

The first derivative of (x^3-x(2x-x^2)) is -5x^4+8x^3+3x^2-4x

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

- 5 x^{4} + 8 x^{3} + 3 x^{2} - 4 x

Solution steps

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

Apply the Product Rule:

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

f = x^{3} - x, g = 2 x - x^{2}

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

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

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

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

Simplify

(3 x^{2} - 1) (2 x - x^{2}) + (2 - 2 x) (x^{3} - x) : - 5 x^{4} + 8 x^{3} + 3 x^{2} - 4 x

= - 5 x^{4} + 8 x^{3} + 3 x^{2} - 4 x

2 y + \frac{d y}{d x} = y^{2} + 1

h (x) = \frac{3}{x ^{2}} + 10 x^{3} - 2 sin (3 x)

\int \frac{2 + 3 x}{x - 3} d x

ln (1 - 7 x), 0

\int \frac{2 x}{3} + 3 d x

What is the derivative of (x^3-x(2x-x^2)) ?
The derivative of (x^3-x(2x-x^2)) is -5x^4+8x^3+3x^2-4x
What is the first derivative of (x^3-x(2x-x^2)) ?
The first derivative of (x^3-x(2x-x^2)) is -5x^4+8x^3+3x^2-4x