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.