derivative of ln|tan(x|)

解答

\frac{d}{d x} (ln ∣ tan (x) ∣)

2 csc (2 x)

求解步骤

\frac{d}{d x} (ln ∣ tan (x) ∣)

使用连锁律:

\frac{1}{∣ tan ( x ) ∣} \frac{d}{d x} (∣ tan (x) ∣)

= \frac{1}{∣ tan ( x ) ∣} \frac{d}{d x} (∣ tan (x) ∣)

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

= \frac{1}{∣ tan ( x ) ∣} \cdot \frac{sec ^{2} ( x ) tan ( x )}{∣ tan ( x ) ∣}

化简

\frac{1}{∣ tan ( x ) ∣} \cdot \frac{sec ^{2} ( x ) tan ( x )}{∣ tan ( x ) ∣} : 2 csc (2 x)

= 2 csc (2 x)

a re a \frac{1}{x + 1}, \frac{( x - 1 )}{2}, 0, 4

a re a x^{2}, 3 x

\int 2 y^{2} cos (9 y) d y

s l o p e y^{5} + 3 x^{2} y^{2} + 5 x^{4} = 49, (- 1, 2)

y^{^{'}} = (t y^{2} - 1) y, y (1) = \frac{1}{2}