derivative f(x)=tan(sec(cos(x)))

解答

导数

f (x) = tan (sec (cos (x)))

- sec^{2} (sec (cos (x))) sec (cos (x)) tan (cos (x)) sin (x)

求解步骤

\frac{d}{d x} (tan (sec (cos (x))))

使用连锁律:

sec^{2} (sec (cos (x))) \frac{d}{d x} (sec (cos (x)))

= sec^{2} (sec (cos (x))) \frac{d}{d x} (sec (cos (x)))

\frac{d}{d x} (sec (cos (x))) = - sec (cos (x)) tan (cos (x)) sin (x)

= sec^{2} (sec (cos (x))) (- sec (cos (x)) tan (cos (x)) sin (x))

化简

= - sec^{2} (sec (cos (x))) sec (cos (x)) tan (cos (x)) sin (x)