(\partial)/(\partial x)(ln(y/(cos(x))))

解

\frac{\partial}{\partial x} (ln (\frac{y}{cos ( x )}))

tan (x)

解答ステップ

\frac{\partial}{\partial x} (ln (\frac{y}{cos ( x )}))

簡素化

ln (\frac{y}{cos ( x )}) : ln (y sec (x))

= \frac{\partial}{\partial x} (ln (y sec (x)))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{y sec ( x )} \frac{\partial}{\partial x} (y sec (x))

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

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

= \frac{1}{y sec ( x )} y sec (x) tan (x)

簡素化

\frac{1}{y sec ( x )} y sec (x) tan (x) : tan (x)

= tan (x)