What is the derivative of x(3x^2-9) ?

The derivative of x(3x^2-9) is 9x^2-9

What is the first derivative of x(3x^2-9) ?

The first derivative of x(3x^2-9) is 9x^2-9

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\frac{d}{d x} (x (3 x^{2} - 9))

9 x^{2} - 9

Solution steps

\frac{d}{d x} (x (3 x^{2} - 9))

Apply the Product Rule:

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

f = x, g = 3 x^{2} - 9

= \frac{d x}{d x} (3 x^{2} - 9) + \frac{d}{d x} (3 x^{2} - 9) x

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

\frac{d}{d x} (3 x^{2} - 9) = 6 x

= 1 \cdot (3 x^{2} - 9) + 6 xx

Simplify

1 \cdot (3 x^{2} - 9) + 6 xx : 9 x^{2} - 9

= 9 x^{2} - 9

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