Differentiation of Function of a Function

If ϒ is a function of u, where u itself is a function of x, then y is called the function of a function, or a composite function of x.

The derivative of the composite function y with respect to x is equal to the product of the derivative of y with respect to u and derivative of u with respect to x. Thus, if y = f(u) and u = f(x), the model will appear as under:

dy/dx= dy/du = du/dx

The above model can be extended to the derivative of a composite function of long chain. Thus, if  ϒ= f(u), u = f(v), and v = f(x), the model will be modified as under: