derivative y^2x+5xy^3+10y^2+8xy

解

導関数

y^{2} x + 5 x y^{3} + 10 y^{2} + 8 x y

2 x y + 15 x y^{2} + 20 y + 8 x

解答ステップ

\frac{d}{d y} (y^{2} x + 5 x y^{3} + 10 y^{2} + 8 x y)

x

を定数として扱う

和/差の法則を適用:

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

= \frac{d}{d y} (y^{2} x) + \frac{d}{d y} (5 x y^{3}) + \frac{d}{d y} (10 y^{2}) + \frac{d}{d y} (8 x y)

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

\frac{d}{d y} (5 x y^{3}) = 15 x y^{2}

\frac{d}{d y} (10 y^{2}) = 20 y

\frac{d}{d y} (8 x y) = 8 x

= 2 x y + 15 x y^{2} + 20 y + 8 x