(\partial)/(\partial y)(4cos(x^2+y^2))

解

\frac{\partial}{\partial y} (4 cos (x^{2} + y^{2}))

- 8 y sin (x^{2} + y^{2})

解答ステップ

\frac{\partial}{\partial y} (4 cos (x^{2} + y^{2}))

x

を定数として扱う

定数を除去:

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

= 4 \frac{\partial}{\partial y} (cos (x^{2} + y^{2}))

連鎖法則を適用:

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

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

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

= 4 (- sin (x^{2} + y^{2}) \cdot 2 y)

簡素化

= - 8 y sin (x^{2} + y^{2})