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In this course you will learn new techniques of integration, further solidify the relationship between differentiation and integration, and be introduced to Common Derivatives and Integrals. Visit tutorial.math.lamar.edu for a complete set of Calculus I Derivatives. Basic Properties/Formulas/Rules. Derivative and Integral Reference Guide. Differentiation Rules. Linearity. Product & Quotient Rules. Chain Rule d dx. [u + v] = u + v d dx. [uv] = u v + v u.Differentiation Formulas d dx k = 0. (1) d dx. [f(x) ± g(x)] = f (x) ± g (x) Integration Formulas. ∫ dx = x + C. (1). ∫ xn dx = xn+1. CALCULUS TRIGONOMETRIC DERIVATIVES AND INTEGRALS. TRIGONOMETRIC DERIVATIVES d dx(sin(x)) = cos(x) · x0 POWER REDUCTION FORMULAS. INVERSE TRIG INTEGRALS. When finding the derivatives of trigonometric functions, non-trigonometric derivative rules are often incorporated, as well as trigonometric derivative Basic Integration Formulas. 1. fkf(u) du = kff(u) du. 3. fau du = u + C DERIVATIVES AND INTEGRALS d d. 2. [u ± v] = u' ± v'. 3. [uv] = uv' + vu'.