(\partial)/(\partial x)(e^x-2-cos(xy))

解

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

y sin (x y) + e^{x}

解答ステップ

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

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

\frac{\partial}{\partial x} (2) = 0

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

= e^{x} - 0 - (- sin (x y) y)

簡素化

= y sin (x y) + e^{x}