(\partial)/(\partial x)(cos(x-y)+(x+y))

解

\frac{\partial}{\partial x} (cos (x - y) + (x + y))

- sin (x - y) + 1

解答ステップ

\frac{\partial}{\partial x} (cos (x - y) + (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} (cos (x - y)) + \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (y)

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

\frac{\partial}{\partial x} (x) = 1

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

= - sin (x - y) + 1 + 0

簡素化

= - sin (x - y) + 1