derivative of-3cot(2xsec(2x))

解答

\frac{d}{d x} (- 3 cot (2 x) sec (2 x))

- 3 (- 2 csc^{2} (2 x) sec (2 x) + 2 sec (2 x) tan (2 x) cot (2 x))

求解步骤

\frac{d}{d x} (- 3 cot (2 x) sec (2 x))

将常数提出:

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

= - 3 \frac{d}{d x} (cot (2 x) sec (2 x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cot (2 x), g = sec (2 x)

= - 3 (\frac{d}{d x} (cot (2 x)) sec (2 x) + \frac{d}{d x} (sec (2 x)) cot (2 x))

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

\frac{d}{d x} (sec (2 x)) = sec (2 x) tan (2 x) \cdot 2

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

化简

= - 3 (- 2 csc^{2} (2 x) sec (2 x) + 2 sec (2 x) tan (2 x) cot (2 x))

\int \frac{1}{3 x + 2} d x

\int_{0}^{2} (x - 3)^{2} - (x - 1)^{2} d x

\int e^{- x} sin^{2} (x) d x

\frac{d x}{d t} = \frac{4 x}{t}, x (1) = 1

t an g e n t \frac{4 x}{x + 1}