(\partial)/(\partial x)(3x^2+ycos(xy))

解

\frac{\partial}{\partial x} (3 x^{2} + y cos (x y))

6 x - y^{2} sin (y x)

解答ステップ

\frac{\partial}{\partial x} (3 x^{2} + y cos (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} (y cos (x y))

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

\frac{\partial}{\partial x} (y cos (x y)) = - y^{2} sin (y x)

= 6 x - y^{2} sin (y x)