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

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

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

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

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

3 x^{2} - 6 x + 2

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x - 1) (x - 2)

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

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

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

= 1 \cdot (x - 1) (x - 2) + (2 x - 3) x

Simplify

1 \cdot (x - 1) (x - 2) + (2 x - 3) x : 3 x^{2} - 6 x + 2

= 3 x^{2} - 6 x + 2

d er i v a t i v e y = 7 x

y^{^{'}} + 5 y = t e^{(4 t)}

\frac{\partial}{\partial x} (3 x^{2} - 4)

\int \frac{9}{9 + e ^{x}} d x

\int \frac{- 1}{2 16 - x} d x

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