What is the derivative of arcsin(coth(x)) ?

The derivative of arcsin(coth(x)) is -(csch^2(x))/(sqrt(-csch^2(x)))

What is the first derivative of arcsin(coth(x)) ?

The first derivative of arcsin(coth(x)) is -(csch^2(x))/(sqrt(-csch^2(x)))

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

- \frac{csch ^{2} ( x )}{- csch ^{2} ( x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

ln (7 x)

y = 6 - x^{2}, y = 26 - 9 x

y^{^{'''}} + y = 0

x \to 9 lim (4 \cdot a + x)

What is the derivative of arcsin(coth(x)) ?
The derivative of arcsin(coth(x)) is -(csch^2(x))/(sqrt(-csch^2(x)))
What is the first derivative of arcsin(coth(x)) ?
The first derivative of arcsin(coth(x)) is -(csch^2(x))/(sqrt(-csch^2(x)))