derivative arcsin(cos(x^8))

解答

导数

arcsin (cos (x^{8}))

- \frac{8 x ^{7} sin ( x ^{8} )}{sin ^{2} ( x ^{8} )}

求解步骤

\frac{d}{d x} (arcsin (cos (x^{8})))

使用连锁律:

\frac{1}{1 - ( cos ( x ^{8} ) ) ^{2}} \frac{d}{d x} (cos (x^{8}))

= \frac{1}{1 - ( cos ( x ^{8} ) ) ^{2}} \frac{d}{d x} (cos (x^{8}))

\frac{d}{d x} (cos (x^{8})) = - sin (x^{8}) \cdot 8 x^{7}

= \frac{1}{1 - ( cos ( x ^{8} ) ) ^{2}} (- sin (x^{8}) \cdot 8 x^{7})

化简

\frac{1}{1 - cos ^{2} ( x ^{8} )} (- sin (x^{8}) \cdot 8 x^{7}) : - \frac{8 x ^{7} sin ( x ^{8} )}{sin ^{2} ( x ^{8} )}

= - \frac{8 x ^{7} sin ( x ^{8} )}{sin ^{2} ( x ^{8} )}