(\partial)/(\partial x)(cos(xy)e^{y^2})

解

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

- e^{y^{2}} y sin (x y)

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

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

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

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

= e^{y^{2}} (- sin (x y) y)

簡素化

= - e^{y^{2}} y sin (x y)