d/(d{z)}(ln((cos({x}){y})^{{z}}))

解

\frac{d}{d z} (ln ((cos (x) y)^{z}))

ln (cos (x) y)

解答ステップ

\frac{d}{d z} (ln ((cos (x) y)^{z}))

連鎖法則を適用:

\frac{1}{( cos ( x ) y ) ^{z}} \frac{d}{d z} ((cos (x) y)^{z})

= \frac{1}{( cos ( x ) y ) ^{z}} \frac{d}{d z} ((cos (x) y)^{z})

\frac{d}{d z} ((cos (x) y)^{z}) = (cos (x) y)^{z} ln (cos (x) y)

= \frac{1}{( cos ( x ) y ) ^{z}} (cos (x) y)^{z} ln (cos (x) y)

簡素化

\frac{1}{( cos ( x ) y ) ^{z}} (cos (x) y)^{z} ln (cos (x) y) : ln (cos (x) y)

= ln (cos (x) y)