(\partial)/(\partial y)(cos(xy)y)

解

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

- x y sin (x y) + cos (x y)

解答ステップ

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

x

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 = cos (x y), g = y

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

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

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

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

簡素化

= - x y sin (x y) + cos (x y)