derivative 1y^2-7y^4(y+9y^3)

解

導関数

1 y^{2} - 7 y^{4} (y + 9 y^{3})

2 y - 7 (63 y^{6} + 5 y^{4})

解答ステップ

\frac{d}{d y} (1 \cdot y^{2} - 7 y^{4} (y + 9 y^{3}))

簡素化

1 \cdot y^{2} - 7 y^{4} (y + 9 y^{3}) : y^{2} - 7 y^{4} (y + 9 y^{3})

= \frac{d}{d y} (y^{2} - 7 y^{4} (y + 9 y^{3}))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d y} (y^{2}) - \frac{d}{d y} (7 y^{4} (y + 9 y^{3}))

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

\frac{d}{d y} (7 y^{4} (y + 9 y^{3})) = 7 (63 y^{6} + 5 y^{4})

= 2 y - 7 (63 y^{6} + 5 y^{4})