derivative y=x^3(9-x^2)

解

導関数

y = x^{3} (9 - x^{2})

27 x^{2} - 5 x^{4}

解答ステップ

\frac{d}{d x} (x^{3} (9 - x^{2}))

積の法則を適用:

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

f = x^{3}, g = 9 - x^{2}

= \frac{d}{d x} (x^{3}) (9 - x^{2}) + \frac{d}{d x} (9 - x^{2}) x^{3}

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

\frac{d}{d x} (9 - x^{2}) = - 2 x

= 3 x^{2} (9 - x^{2}) + (- 2 x) x^{3}

簡素化

3 x^{2} (9 - x^{2}) + (- 2 x) x^{3} : 27 x^{2} - 5 x^{4}

= 27 x^{2} - 5 x^{4}