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## Homework Statement

y=arccoth(x), find the derivative

## Homework Equations

cothx - coshx/sinhx

## The Attempt at a Solution

y = arccoth(x)

x = coth(y)

= cosh(y)/sinh(y)

quotient rule = (sinh(y)*sinh(y))-(cosh(y)*cosh(y))/(sinh(y))^2

= sinh^2(y) - cosh^2(y)/sinh^2(y)

x= -1/sinh^2(y)

this is what i got which is the derivative of coth, but no the inverse. Is there a way to go from here and rearrange it back to y =