(\partial)/(\partial x)(x^2sin(3xy))

解

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

2 x sin (3 x y) + cos (3 x y) \cdot 3 y x^{2}

解答ステップ

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

y

を定数として扱う

積の法則を適用:

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

f = x^{2}, g = sin (3 x y)

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

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

\frac{\partial}{\partial x} (sin (3 x y)) = cos (3 x y) \cdot 3 y

= 2 x sin (3 x y) + cos (3 x y) \cdot 3 y x^{2}