Derivatives of hyperbolic trigonometric functions

Sep 2011
393
8
Mumbai (Bombay),Maharashtra,India
(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.
 

topsquark

Forum Staff
Jan 2006
11,568
3,453
Wellsville, NY
(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
 
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