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This lecture covers the history and development of differential calculus, starting with the controversy over the invention of infinitesimal calculus by Leibniz and Newton. It explains the concept of tangent to a curve, derivative calculation, and the limit of the slope of lines. Examples include the slope of a line, parabola, and absolute value function. The lecture also delves into the derivative of various functions, including the power function, exponential function, and natural logarithm. It concludes with the derivatives of trigonometric and reciprocal trigonometric functions.
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