(\partial)/(\partial y)(xycos(yz))

解

\frac{\partial}{\partial y} (x y cos (yz))

x (cos (yz) - yz sin (yz))

解答ステップ

\frac{\partial}{\partial y} (x y cos (yz))

x, z

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

積の法則を適用:

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

f = y, g = cos (yz)

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

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

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

= x (1 \cdot cos (yz) + (- sin (yz) z) y)

簡素化

= x (cos (yz) - yz sin (yz))