Question

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

Answer 1

Answer:

Step-by-step 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.

$1=coshy \frac{dy}{dx} \\\frac{dy}{dx}=\frac{1}{coshy}$

In hyperbolic functions we have relation as

$cosh^2 x- sinh^2 x =1\\coshy = \sqrt{1+sinh^2 y} =\sqrt{1+x^2}$

Hence derivative = $\frac{1}{\sqrt{1+x^2} }$