What can be said about differentiation of a constant with respect to a constant & differentiation of a variable with respect to a constant?

1 Answer
Dec 21, 2017

Please see below.

Explanation:

One of the definition of the derivative of function f with respect to function g is

(df)/(dg) = lim_(hrarr0) (f(x+h)-f(x))/(g(x+h)-g(x))

If g(x) is a constant function, then g(x+h) = g(x) for all x and all h, so the denominator is always 0 and no limit exists.

This is true regardless of whether f(x) is constant or non-constant.

Another definition

(df)/(dg) = (df)/dx * 1/((dg)/dx)

But if g is constant then (dg)/dx = 0, so the second factor is not defined.
Again whether f is constant or variable, no derivative exists.