derivative y=3x^2(x-3)^3

解

導関数

y = 3 x^{2} (x - 3)^{3}

3 (2 x (x - 3)^{3} + 3 (x - 3)^{2} x^{2})

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

= 3 (2 x (x - 3)^{3} + 3 (x - 3)^{2} x^{2})