Find The Derivative of y = sinh^-1 (1/x)

[KAISER91]

Homework Statement

Differentiate

y = sinh^-1 (1/x)

Homework Equations

The Attempt at a Solution

y' = 1 / sqrt 1 + (1/x)^2 x -1/x^2


Really confused with this.

Is there a different method to this like;


y = sinh^-1 (1/x)

sinh y = 1/x


Thanks

 

[phyzguy]

You're on the right track with implicit differentiation. Keep going down this path:
$$sinh(y)=\frac{1}{x}$$
$$cosh(y) dy = -\frac{1}{x^2}dx$$
$$cosh(y)\frac{dy}{dx} = -\frac{1}{x^2}$$
$$y'=-\frac{1}{cosh(y) x^2}$$
Now express cosh(y) in terms of x using identities and you're done.