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

The derivative of (-x^2+2x(3x+2)(x-1)) is -12x^3+21x^2-4

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

The first derivative of (-x^2+2x(3x+2)(x-1)) is -12x^3+21x^2-4

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

- 12 x^{3} + 21 x^{2} - 4

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((3 x + 2) (x - 1)) = 6 x - 1

= (- 2 x + 2) (3 x + 2) (x - 1) + (6 x - 1) (- x^{2} + 2 x)

Simplify

(- 2 x + 2) (3 x + 2) (x - 1) + (6 x - 1) (- x^{2} + 2 x) : - 12 x^{3} + 21 x^{2} - 4

= - 12 x^{3} + 21 x^{2} - 4

f (x) = 3 x^{2}, (1, 3)

y^{^{'}} = \frac{e ^{x}}{y}

\int_{1}^{5} \frac{2}{x} d x

x \to 0 lim (\frac{20}{1 + x})

\int cos (5)

What is the derivative of (-x^2+2x(3x+2)(x-1)) ?
The derivative of (-x^2+2x(3x+2)(x-1)) is -12x^3+21x^2-4
What is the first derivative of (-x^2+2x(3x+2)(x-1)) ?
The first derivative of (-x^2+2x(3x+2)(x-1)) is -12x^3+21x^2-4