Find dy/dx For Inverse Hyperbolic Functions?

Question

Find dy/dx For Inverse Hyperbolic Function

y = sinh^(-1) (cosh2x)

Answer 1

y = arcsinh(cosh2x)

Take sinh to each side

sinhy = sinh(arcsinh(cosh2x)

Since sinh and arcsinh are inverse functions

sinhy = cosh2x

Take derivative to each side with respective x

coshy dy / dx = sinh2x (2)

dy / dx = 2sinh2x / coshy.

Answer 2

The inverse hyperbolic function is y = sinh^(-1) (cosh2x).