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

The derivative of (x^2-2x)(2x-x^2) is -4x^3+12x^2-8x

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

The first derivative of (x^2-2x)(2x-x^2) is -4x^3+12x^2-8x

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derivative of

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

- 4 x^{3} + 12 x^{2} - 8 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(2 x - 2) (2 x - x^{2}) + (2 - 2 x) (x^{2} - 2 x) : - 4 x^{3} + 12 x^{2} - 8 x

= - 4 x^{3} + 12 x^{2} - 8 x

\frac{\partial}{\partial t} (t e^{s t})

\frac{d}{d x} ((x - 1) tan (x) + x sin (π x))

(2 x y) d x + (x^{2} - 1) d y = 0

\frac{8}{x ^{6}}

\frac{d}{d x} (\frac{3}{( x ^{2} - 5 x ) ^{2}})

What is the derivative of (x^2-2x)(2x-x^2) ?
The derivative of (x^2-2x)(2x-x^2) is -4x^3+12x^2-8x
What is the first derivative of (x^2-2x)(2x-x^2) ?
The first derivative of (x^2-2x)(2x-x^2) is -4x^3+12x^2-8x