If the function does not depend on the indicated parameter, why is the derivative zero?

Question

If we have the derivative $\dfrac{dy}{dx}$ but $y$ doest not depend on $x$, why is $\dfrac{dy}{dx} = 0 ?$

I think that a possible correct thought is that if we see the derivative as rate of change, is clear that since the variable $x$ does not affect $y$, then no change occurs and therefore the derivative is zero.

But, what is the interpretation if we see the derivative as slope ?

Answer 1

If you think of $y$ as a function not depending on $x$, then what you're saying is that $y$ is a constant, for any value of $x$. Pictorially, that means the graph is a horizontal line at some height $c \in \mathbb{R}$. What is the slope of a horizontal line? (Zero!)