# Thread: Derivatives of hyperbolic trigonometric functions

1. ## Derivatives of hyperbolic trigonometric functions

(a) If $cosh (y) = x + x^3y,$

then at the point (1, 0) we y'=
A. 0, B. −1, C. 1, D. 3, E. Does not exist.
This is multiple choice question.
The answer is (b). I don't know how it is computed. If any member explain me, it would be good help.

2. ## Re: Derivatives of hyperbolic trigonometric functions

Originally Posted by Vinod
(a) If $cosh (y) = x + x^3y,$

then at the point (1, 0) we y'=
A. 0, B. −1, C. 1, D. 3, E. Does not exist.
This is multiple choice question.
The answer is (b). I don't know how it is computed. If any member explain me, it would be good help.
$\displaystyle \frac{d}{dx}( cosh(y) ) = sinh(y) \cdot \frac{dy}{dx}$

So we know that
$\displaystyle sinh(y) \cdot \frac{dy}{dx} = 1 + 3x^2 y + x^3 \frac{dy}{dx}$

Now, for y = 0 we have $\displaystyle sinh(0) = \frac{e^0 - e^{-0}}{2} = 0$

So what is dy/dx?

-Dan