derivative of ({z}(x)(6x-3x^2))

解

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

\frac{d}{d x} (z (x)) (6 x - 3 x^{2}) + (6 - 6 x) z (x)

解答ステップ

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

積の法則を適用:

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

f = z (x), g = 6 x - 3 x^{2}

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

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

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