derivative y=3csc^2(5x)^3

解答

导数

y = 3 csc^{2} (5 x)^{3}

- 90 csc^{6} (5 x) cot (5 x)

求解步骤

\frac{d}{d x} (3 (csc^{2} (5 x))^{3})

化简

3 (csc^{2} (5 x))^{3} : 3 csc^{6} (5 x)

= \frac{d}{d x} (3 csc^{6} (5 x))

将常数提出:

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

= 3 \frac{d}{d x} (csc^{6} (5 x))

使用连锁律:

6 (csc (5 x))^{5} \frac{d}{d x} (csc (5 x))

= 6 (csc (5 x))^{5} \frac{d}{d x} (csc (5 x))

\frac{d}{d x} (csc (5 x)) = - cot (5 x) csc (5 x) \cdot 5

= 3 \cdot 6 (csc (5 x))^{5} (- cot (5 x) csc (5 x) \cdot 5)

化简

3 \cdot 6 csc^{5} (5 x) (- cot (5 x) csc (5 x) \cdot 5) : - 90 csc^{6} (5 x) cot (5 x)

= - 90 csc^{6} (5 x) cot (5 x)

t an g e n t y = x^{3} - 2 x + 2 (3.23)

\frac{d}{d x} (4 x^{3} - 5 x^{2} + 3 x - 5)

\frac{d}{d x} (arctan (2 x - 1))

x y^{^{'}} + 36 y = \frac{1}{x}

a re a sin (x), cos (x), [0, \frac{π}{4}]