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

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

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

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

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

4 - 2 x

Solution steps

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

Apply the Product Rule:

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

f = x, g = 4 - x

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

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

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

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

Simplify

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

= 4 - 2 x

\int 3 cos (θ) d θ

\frac{d}{d x} (920 + 2 x - 0.2 x^{2} + 0.7 x^{3})

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

\frac{\partial}{\partial x} (e^{x yz})

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