derivative y=(-1)/(3sin^3(x))

解答

导数

y = \frac{- 1}{3 sin ^{3} ( x )}

\frac{cos ( x )}{sin ^{4} ( x )}

求解步骤

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

化简

\frac{- 1}{3 sin ^{3} ( x )} : - \frac{1}{3 sin ^{3} ( x )}

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

- \frac{3}{( sin ( x ) ) ^{4}} \frac{d}{d x} (sin (x))

= - \frac{3}{( sin ( x ) ) ^{4}} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

= - \frac{1}{3} (- \frac{3}{( sin ( x ) ) ^{4}} cos (x))

化简

- \frac{1}{3} (- \frac{3}{sin ^{4} ( x )} cos (x)) : \frac{cos ( x )}{sin ^{4} ( x )}

= \frac{cos ( x )}{sin ^{4} ( x )}

\int (3 t) d t

\int x + tan (x) d x

x \to \infty lim (\frac{3 x ^{2} + 5 x ^{3}}{2 x ^{2} - 3 x})

in v erse l a pl a ce \frac{( s )}{( s ^{2} + 6 s + 25 )}

\frac{d}{d x} ((4 x + 6) (9 x - 5))