derivative f(x)=arcsin(x^6)

解

導関数

f (x) = arcsin (x^{6})

\frac{6 x ^{5}}{1 - x ^{12}}

解答ステップ

\frac{d}{d x} (arcsin (x^{6}))

連鎖法則を適用:

\frac{1}{1 - ( x ^{6} ) ^{2}} \frac{d}{d x} (x^{6})

= \frac{1}{1 - ( x ^{6} ) ^{2}} \frac{d}{d x} (x^{6})

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{1}{1 - ( x ^{6} ) ^{2}} \cdot 6 x^{5}

簡素化

\frac{1}{1 - ( x ^{6} ) ^{2}} \cdot 6 x^{5} : \frac{6 x ^{5}}{1 - x ^{12}}

= \frac{6 x ^{5}}{1 - x ^{12}}