What is the derivative of x(x-4) ?

The derivative of x(x-4) is 2x-4

What is the first derivative of x(x-4) ?

The first derivative of x(x-4) is 2x-4

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\frac{d}{d x} (x (x - 4))

2 x - 4

Solution steps

\frac{d}{d x} (x (x - 4))

Apply the Product Rule:

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

f = x, g = x - 4

= \frac{d x}{d x} (x - 4) + \frac{d}{d x} (x - 4) x

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

\frac{d}{d x} (x - 4) = 1

= 1 \cdot (x - 4) + 1 \cdot x

Simplify

1 \cdot (x - 4) + 1 \cdot x : 2 x - 4

= 2 x - 4