(\partial)/(\partial x)(-ysec^2(x))

解

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

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

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

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

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

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

= - y \cdot 2 sec (x) sec (x) tan (x)

簡素化

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

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