(\partial)/(\partial y)(e^xsec^2(y))

解

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

2 e^{x} sec^{2} (y) tan (y)

解答ステップ

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

x

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

2 sec (y) \frac{\partial}{\partial y} (sec (y))

= 2 sec (y) \frac{\partial}{\partial y} (sec (y))

\frac{\partial}{\partial y} (sec (y)) = sec (y) tan (y)

= e^{x} \cdot 2 sec (y) sec (y) tan (y)

簡素化

e^{x} \cdot 2 sec (y) sec (y) tan (y) : 2 e^{x} sec^{2} (y) tan (y)

= 2 e^{x} sec^{2} (y) tan (y)