During differentiation the dependent variable of a function is differentiated w.r.t. some variable instead of the function itself. Why then do we call the outcome of differentiation the derivative of the function rather than calling it the derivative of the dependent variable.
2026-04-18 02:45:23.1776480323
When calculating derivative of a function f why do we differentiate the function's dependent variable?
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We don't. We say that we are differentiating the function with respect to the variable.
You are right to observe that the choice of variable is integral to the operation. The reason for this is that we are measuring how tiny changes in one thing affect the other - in your example, how tiny changes in $x$ affect $f(x)$.
You say that "the dependent variable is used instead of the function" but if that were strictly true, the result you got would be the same irrespective of what the function was. In actual fact what we use is the structure of the function containing the variable, and we adjust it according to certain rules in order to transform the function $f$ into its derivative $f'$.