Explore the fundamental concepts and techniques of calculus in this comprehensive 2.5-hour tutorial on determining derivatives. Master logarithmic differentiation, learn the derivatives of exponential and trigonometric functions, and understand key rules such as the sum/difference, product, quotient, and chain rules. Delve into topics like implicit differentiation, the limit definition of derivatives, and the derivative as a function. Practice with various examples, including higher-order derivatives, rates of change, tangent lines, and derivatives of inverse trigonometric functions. Gain a solid foundation in differentiation techniques essential for advanced mathematical analysis and problem-solving.