derivative ln(tan(x^3))

解

導関数

ln (tan (x^{3}))

3 x^{2} sec^{2} (x^{3}) cot (x^{3})

解答ステップ

\frac{d}{d x} (ln (tan (x^{3})))

連鎖法則を適用:

\frac{1}{tan ( x ^{3} )} \frac{d}{d x} (tan (x^{3}))

= \frac{1}{tan ( x ^{3} )} \frac{d}{d x} (tan (x^{3}))

\frac{d}{d x} (tan (x^{3})) = sec^{2} (x^{3}) \cdot 3 x^{2}

= \frac{1}{tan ( x ^{3} )} sec^{2} (x^{3}) \cdot 3 x^{2}

簡素化

\frac{1}{tan ( x ^{3} )} sec^{2} (x^{3}) \cdot 3 x^{2} : 3 x^{2} sec^{2} (x^{3}) cot (x^{3})

= 3 x^{2} sec^{2} (x^{3}) cot (x^{3})