How can I build intuition for derivatives beyond the tangent slope?

[Evelyn_L]

I'm a first-year engineering student struggling to grasp the fundamental concept of the derivative in calculus. I can mechanically find derivatives using the power rule, but I don't have an intuitive understanding of what the derivative actually represents beyond "slope of a tangent line." When my professor talks about instantaneous rate of change in the context of physics problems, it feels abstract and disconnected from the formulas. For those who truly mastered calculus, how did you build that conceptual bridge? Are there specific real-world analogies, visualizations, or resources that finally made the core ideas of limits and derivatives click for you?