(\partial)/(\partial y)(5cos(xy^2))

解

\frac{\partial}{\partial y} (5 cos (x y^{2}))

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

解答ステップ

\frac{\partial}{\partial y} (5 cos (x y^{2}))

x

を定数として扱う

定数を除去:

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

= 5 \frac{\partial}{\partial y} (cos (x y^{2}))

連鎖法則を適用:

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

= - sin (x y^{2}) \frac{\partial}{\partial y} (x y^{2})

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

= 5 (- sin (x y^{2}) \cdot 2 x y)

簡素化

= - 10 x y sin (x y^{2})