# Thread: Derivative of Hyperbolic Function

1. ## Derivative of Hyperbolic Function

I must find d/dx of the function in the picture. I get a different answer than the textbook. Can someone explain, based on my picture, what I did wrong?

2. ## Re: Derivative of Hyperbolic Function

The hyperbolic half-angle formula:

$\sinh(x) = \text{sgn}(x)\sqrt{\dfrac{\cosh(2x)-1}{2}}$

Square both sides, and you find that your answer is equal to the textbook's answer. Check out hyperbolic trig identities. Better yet, try to prove them on your own.

3. ## Re: Derivative of Hyperbolic Function

Originally Posted by nycmath
I must find d/dx of the function in the picture. I get a different answer than the textbook. Can someone explain, based on my picture, what I did wrong?
Is it possible that the two solution are equivalent?

4. ## Re: Derivative of Hyperbolic Function

Thanks. Great to know that my answer is correct.

5. ## Re: Derivative of Hyperbolic Function

I squared both sides and found out that my answer matches the textbook answer. I never knew that trig half-angle formulas extended into the hyperbolic topic.