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

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

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,

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

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

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