Question

Question 2 Find the derivative of the inverse hyperbolic function sinh-'(x), using implicit differentiation.

Answer 1

Explanation:

To find the derivative of inverse hyperbolic function sinh-'(x),

Let
`y =sinh-'(x),\\x = sinhy`

This is an implicit function. Now differentiate both the sides.

`1=coshy (dy)/(dx) \\(dy)/(dx)=(1)/(coshy)`

In hyperbolic functions we have relation as

`cosh^2 x- sinh^2 x =1\\coshy = √(1+sinh^2 y) =√(1+x^2)`

Hence derivative =
`(1)/(√(1+x^2) )`