So what exactly is a derivative? Is that the EQUATION of the line tangent to any point on a curve? So there are 2 equations? One for the actual curve, the other for the line tangent to some point on the curve? How can the equation of the tangent line be the same equation throughout the curve?
[Math] Derivative of a function is the equation of the tangent line
calculusintegration
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Best Answer
The derivative of a function at a point is the slope of the tangent line at that point, not the line's equation. The function $f'(x)$ tells you this slope for each point in the domain of $f$ where a non-vertical tangent line exists.