How to find the derivative of one output quantity with respect to another output quantity

I want to consult that how to find the derivative of one output quantity with respect to another output quantity. For example, output module 1 is force and output module 2 is time, and I want to find the derivative of module 1 with respect to module 2. Thank you for your help.

Answer 1

[Chunru]

x = 0:32;
y = sin(2*pi*x/16);
d = gradient(y)./gradient(x);

plot(x, y, 'r-', x, d, 'b-')

Answer 2

[John D'Errico]

Basic calculus. Each module must be a function of SOMETHING else, thu some other parameter. What parameter is controlling them? For example, suppose I have two modules.

Use this basic rule for differentiation:

dx/dy = (dx/dt)/(dy/dt)

Now lets try it. I'll make up some arbitrary relations to put in the two modules.

module1 = @(p) sin(p);
module2 = @(p) cos(p);

Suppose I want to compute the derivative of module1, with respect to module 2, at the point where p=1.

dp = 1e-8;
p0 = 1;
dm1dm2 = ((module1(p0 + dp) - module1(p0))/dp) / ((module2(p0 + dp) - module2(p0))/dp)

dm1dm2 = -0.6421