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

The derivative of (3x-x^2(3-x-x^2)) is 4x^3-6x^2-12x+9

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

The first derivative of (3x-x^2(3-x-x^2)) is 4x^3-6x^2-12x+9

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

4 x^{3} - 6 x^{2} - 12 x + 9

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(3 - 2 x) (3 - x - x^{2}) + (- 2 x - 1) (3 x - x^{2}) : 4 x^{3} - 6 x^{2} - 12 x + 9

= 4 x^{3} - 6 x^{2} - 12 x + 9

\int \frac{x ^{2} + 84 x + 84}{x ^{3} - 4 x} d x

\frac{\partial}{\partial x} (3 x^{4} + 5 x^{4} + 9 x y)

\frac{\partial}{\partial s} (\frac{7}{s})

h (x) = x^{3} + 4 x^{4}

f (t) = sin (2 t)

What is the derivative of (3x-x^2(3-x-x^2)) ?
The derivative of (3x-x^2(3-x-x^2)) is 4x^3-6x^2-12x+9
What is the first derivative of (3x-x^2(3-x-x^2)) ?
The first derivative of (3x-x^2(3-x-x^2)) is 4x^3-6x^2-12x+9