derivative of pix(x-3)

解

\frac{d}{d x} (π x (x - 3))

π (2 x - 3)

解答ステップ

\frac{d}{d x} (π x (x - 3))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= π \frac{d}{d x} (x (x - 3))

積の法則を適用:

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

f = x, g = x - 3

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

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

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

= π (1 \cdot (x - 3) + 1 \cdot x)

簡素化

π (1 \cdot (x - 3) + 1 \cdot x) : π (2 x - 3)

= π (2 x - 3)