derivative of csc^2(1-2x)

解答

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

4 csc^{2} (1 - 2 x) cot (1 - 2 x)

求解步骤

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

使用连锁律:

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

= 2 csc (1 - 2 x) \frac{d}{d x} (csc (1 - 2 x))

\frac{d}{d x} (csc (1 - 2 x)) = 2 cot (1 - 2 x) csc (1 - 2 x)

= 2 csc (1 - 2 x) \cdot 2 cot (1 - 2 x) csc (1 - 2 x)

化简

2 csc (1 - 2 x) \cdot 2 cot (1 - 2 x) csc (1 - 2 x) : 4 csc^{2} (1 - 2 x) cot (1 - 2 x)

= 4 csc^{2} (1 - 2 x) cot (1 - 2 x)

x \to - 1 lim (3 x^{4} - 6 x + 1)

\int 3 x^{2} + 2 x d x

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

x \to - 6 + lim (x + 6)

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