What is the derivative of the hyperbolic tangent equation?

Question

Suppose I have the following hyperbolic tangent equation:

(1-e^(-(2x)))/(1+e^(-(2x)))

 

What will be the derivative of this equation?

Answer 1

Hi Maddy,

             It's similar to the derivative of tan(x) d/dx(tanh(x))=sech²(x). 

You can derive the by starting with d/dx(sinh(x)/cosh(x)) and just grind it out with the quotient rule. Remember that cosh²(x)-sinh²(x)=1.

 

Hope this helps

 

Jim