What is the derivative of f(x)=x(2-x)(x+3) ?

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

What is the first derivative of f(x)=x(2-x)(x+3) ?

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

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derivative of

f (x) = x (2 - x) (x + 3)

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = (2 - x) (x + 3)

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

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

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

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

Simplify

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

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

y^{^{'}} = 4 y + y^{4}, y (0) = 1

\frac{d}{d x} (- 15 sin (5 x))

\frac{d}{d x} (4 x^{3} - 168 x^{2} + 1728 x)

x \to - 2 + lim (\frac{x - 1}{3 x + 6})

\int cot^{2} (x) d x

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