(\partial)/(\partial x)(3x^2+5y^7+9xy)

解

\frac{\partial}{\partial x} (3 x^{2} + 5 y^{7} + 9 x y)

6 x + 9 y

解答ステップ

\frac{\partial}{\partial x} (3 x^{2} + 5 y^{7} + 9 x y)

y

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (5 y^{7}) + \frac{\partial}{\partial x} (9 x y)

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

\frac{\partial}{\partial x} (5 y^{7}) = 0

\frac{\partial}{\partial x} (9 x y) = 9 y

= 6 x + 0 + 9 y

簡素化

= 6 x + 9 y