derivative f(x)=ln|cot(3*x)|

解答

导数

f (x) = ln ∣ cot (3 \cdot x) ∣

- 3 csc^{2} (3 x) tan (3 x)

求解步骤

\frac{d}{d x} (ln ∣ cot (3 x) ∣)

使用连锁律:

\frac{1}{∣ cot ( 3 x ) ∣} \frac{d}{d x} (∣ cot (3 x) ∣)

= \frac{1}{∣ cot ( 3 x ) ∣} \frac{d}{d x} (∣ cot (3 x) ∣)

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

= \frac{1}{∣ cot ( 3 x ) ∣} (- \frac{3 csc ^{2} ( 3 x ) cot ( 3 x )}{∣ cot ( 3 x ) ∣})

化简

\frac{1}{∣ cot ( 3 x ) ∣} (- \frac{3 csc ^{2} ( 3 x ) cot ( 3 x )}{∣ cot ( 3 x ) ∣}) : - 3 csc^{2} (3 x) tan (3 x)

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

((3 x^{2} + 3 x + 4)^{^{'}} (3 x^{2} + 6 x)^{^{'}})^{^{'}}

\int e^{t a n (2 x)} sec^{2} (2 x) d x

\int \frac{1}{3 x ^{4}} d x

\int_{- 1}^{1} \frac{1}{2} (4 - 4 x^{2})^{2} d x

\frac{\partial}{\partial t} (\frac{s - 3 r}{t})