Question

If differentiation of a constant with respect to a variable is 0 , then differentiation of a variable with respect to a constant is infinity?

Yes or no I'm confused

Answer 1

Dear student,
you are right. Answer is yes.

Explanation for your first question is:

The derivative of a function represents the instantaneous rate of change (slope of the tangent line) at a given value of x. Since the graph of f(x) = C has a slope of 0 for all x, its derivative is 0 for all x.
also,

Derivative of function f with respect to x is defined as delta change in f with delta change in x . Basically the rate at with f changes due to change in x.
the constant function does not change with any change in other variable (since it is constant function) . As rate of change is zero hence derivative is 0.

Explanation for your next question:

dy/dx in words means change in y with one unit small change in x so in cases where x is a constant that simply means there is no change in x against which you would otherwise look at change in y so simply tht implies dx=0 and hence dy/dx is not defined.

I hope you understand.