textbook-theory · English
Products and Powers
A three-page calculus lecture note covering two fundamental rules of differentiation. The first section derives and applies the power rule for composite functions, showing how d/dx[(f(x))^n] = n(f(x))^(n-1) * f'(x), with worked examples including trigonometric polynomials. The second section introduces the product rule (Leibniz rule), h'(x) = f'(x)g(x) + f(x)g'(x), demonstrating its necessity and consistency with the power rule through multiple examples including verification that the derivative of a constant is zero.
calculuspower ruleproduct ruledifferentiation