1st, 2nd and 3rd derivatives of seven parameter double sigmoid function

[Ade Sol]

I want the 1st, 2nd and 3rd derivatives of the following seven parameter double sigmoid function

Y = a + b /(1 + exp(-c(X-d))) – e/(1 + exp(-f(X-g)))

a,b,c,d,e,f,g are the equation parameters.

I can go as far as the 1st derivative:

If z = (1 + exp(-c(X-d))) and h = (1 + exp(-f(X-g)))

dY/dX = b(-c z)/(1+z)^2 – e(-f h)^2

I am not even sure if this is the correct 1st derivative of the above equation.

I also need some hand for 2nd and 3rd derivative. Very long time since the last maths class.

Cheers,

 

[BGM]

There should be several online calculator to help you to check the tedious derivatives for you. For example, you may try to search

d/dX [a + b /(1 + exp(-c*(X-d))) – e/(1 + exp(-f*(X-g)))]

in www.wolframalpha.com