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History, purpose, meaning of derivatives (differentiation)

Leibniz’s Discovery of derivatives (Slope of tangent)

Newton’s Discovery of derivatives (Rate of Change)

First Principle of Derivatives

Derivative of constant using first principle (Example 11)

Derivative of x using first principle

Derivative of $x^2$ using first principle (Example 10)

Derivative of $x^3$ using first principle

Example 9. Find the derivative of $f(x) = 10x$.

Example 12. Find the derivative of  $f(x) = \frac{1}{x}$