(\partial)/(\partial x)(x^2sin(xy+z))

解

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

2 x sin (x y + z) + cos (x y + z) y x^{2}

解答ステップ

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

y, z

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 (x y + z)

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

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

\frac{\partial}{\partial x} (sin (x y + z)) = cos (x y + z) y

= 2 x sin (x y + z) + cos (x y + z) y x^{2}