(\partial)/(\partial y)(x^2ycos(z/t))

解

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

x^{2} cos (\frac{z}{t})

解答ステップ

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

x, z, t

を定数として扱う

定数を除去:

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

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

共通の導関数を適用:

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

= x^{2} cos (\frac{z}{t}) \cdot 1

簡素化

= x^{2} cos (\frac{z}{t})