derivative of sqrt(cos(e^{x^4sin(x))})

解答

\frac{d}{d x} (cos (e^{x^{4} s i n (x)}))

- \frac{e ^{x^{4} s i n (x)} sin ( e ^{x^{4} s i n (x)} ) ( 4 x ^{3} sin ( x ) + x ^{4} cos ( x ) )}{2 cos ( e ^{x^{4} s i n (x)} )}

求解步骤

\frac{d}{d x} (cos (e^{x^{4} s i n (x)}))

使用连锁律:

\frac{1}{2 cos ( e ^{x^{4} s i n (x)} )} \frac{d}{d x} (cos (e^{x^{4} s i n (x)}))

= \frac{1}{2 cos ( e ^{x^{4} s i n (x)} )} \frac{d}{d x} (cos (e^{x^{4} s i n (x)}))

\frac{d}{d x} (cos (e^{x^{4} s i n (x)})) = - sin (e^{x^{4} s i n (x)}) e^{x^{4} s i n (x)} (4 x^{3} sin (x) + cos (x) x^{4})

= \frac{1}{2 cos ( e ^{x^{4} s i n (x)} )} (- sin (e^{x^{4} s i n (x)}) e^{x^{4} s i n (x)} (4 x^{3} sin (x) + cos (x) x^{4}))

化简

\frac{1}{2 cos ( e ^{x^{4} s i n (x)} )} (- sin (e^{x^{4} s i n (x)}) e^{x^{4} s i n (x)} (4 x^{3} sin (x) + cos (x) x^{4})) : - \frac{e ^{x^{4} s i n (x)} sin ( e ^{x^{4} s i n (x)} ) ( 4 x ^{3} sin ( x ) + x ^{4} cos ( x ) )}{2 cos ( e ^{x^{4} s i n (x)} )}

= - \frac{e ^{x^{4} s i n (x)} sin ( e ^{x^{4} s i n (x)} ) ( 4 x ^{3} sin ( x ) + x ^{4} cos ( x ) )}{2 cos ( e ^{x^{4} s i n (x)} )}

\int \frac{x ^{6} - 3 x}{x ^{4}} d x

s im pl i f y \frac{y ^{4}}{8} + \frac{1}{4 y ^{2}}

\frac{d}{d x} (- \frac{6 x}{1 - 3 x ^{2}})

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

\int sin (2 y) d y