(\partial)/(\partial x)(xyz-z-sin(x+y))

解

\frac{\partial}{\partial x} (x yz - z - sin (x + y))

yz - cos (x + y)

解答ステップ

\frac{\partial}{\partial x} (x yz - z - sin (x + y))

y, z

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} (x yz) - \frac{\partial}{\partial x} (z) - \frac{\partial}{\partial x} (sin (x + y))

\frac{\partial}{\partial x} (x yz) = yz

\frac{\partial}{\partial x} (z) = 0

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

= yz - 0 - cos (x + y)

簡素化

= yz - cos (x + y)