Video Summary

Differential calculus centers around finding derivatives, which represent instantaneous rates of change. Derivative rules and formulas provide efficient methods for calculating these rates without resorting to the limit definition. Key rules include the power rule (for polynomial terms), the constant multiple rule (allowing scalar multiplication to be factored out), the sum/difference rule (derivatives of sums or differences are the sums or differences of derivatives), the product rule (for the derivative of a product of functions), and the quotient rule (for the derivative of a quotient of functions). The chain rule is crucial for differentiating composite functions, expressing the derivative as the product of the outer function's derivative (with the inside function untouched) and the inner function's derivative. These rules, along with derivatives of standard functions like trigonometric functions (sine, cosine, tangent, etc.), exponential functions, and logarithmic functions, form a toolkit for differentiating a wide range of functions.