derivative of ln(coth(x))

解答

\frac{d}{d x} (ln (coth (x)))

- csch^{2} (x) tanh (x)

求解步骤

\frac{d}{d x} (ln (coth (x)))

使用连锁律:

\frac{1}{coth ( x )} \frac{d}{d x} (coth (x))

= \frac{1}{coth ( x )} \frac{d}{d x} (coth (x))

\frac{d}{d x} (coth (x)) = - csch^{2} (x)

= \frac{1}{coth ( x )} (- csch^{2} (x))

化简

\frac{1}{coth ( x )} (- csch^{2} (x)) : - csch^{2} (x) tanh (x)

= - csch^{2} (x) tanh (x)

\int \frac{cos ( 5 x )}{e ^{s i n (5 x)}} d x

\frac{d y}{d x} = 9 x + y

x \to 0 lim ((x - 1)^{2})

\int_{0}^{\infty} x^{2} e^{- x} d x

s l o p e (3.5) (2.6)