derivative y=csc^3(2x)

解答

导数

y = csc^{3} (2 x)

- 6 csc^{3} (2 x) cot (2 x)

求解步骤

\frac{d}{d x} (csc^{3} (2 x))

使用连锁律:

3 (csc (2 x))^{2} \frac{d}{d x} (csc (2 x))

= 3 (csc (2 x))^{2} \frac{d}{d x} (csc (2 x))

\frac{d}{d x} (csc (2 x)) = - cot (2 x) csc (2 x) \cdot 2

= 3 (csc (2 x))^{2} (- cot (2 x) csc (2 x) \cdot 2)

化简

3 csc^{2} (2 x) (- cot (2 x) csc (2 x) \cdot 2) : - 6 csc^{3} (2 x) cot (2 x)

= - 6 csc^{3} (2 x) cot (2 x)

\frac{d}{d x} ((a x + b) e^{- x})

\int [x (x^{2} - 1) + csc^{2} (x)] d x

d er i v a t i v e 4 sin (x) sin (x)

in v erse l a pl a ce \frac{s + 5}{s ^{2} + 5 s + 9}

y^{^{''}} + 4 y = t^{2} + 3 e^{t}, y (0) = 0, y^{^{'}} (0) = 2