Mat271 - Study guides, Class notes & Summaries

derivative RVW * d/dx (x^n) = n * x ^ (n-1) * product rule: d/dx(uv) = u'v + uv' * quotient rule: d/dx (f(x) / g(x)) = [gf' - fg']/ g^2 * chain rule: dy/dx = dy/du * du/dx trig derivative RVW * d/dx (sin x) = cos x * d/dx (cos x) = - sin x * d/dx (tan x) = sec^2 x * d/dx (csc x) = - csc x * cot x * d/dx (sec x) = sec x * tan x * d/dx (cot x) = - csc^2 x * d/dx (arcsin x) = 1 / [1 - x^2]^1/2 * d/dx (arctan x) = 1 / [1 + x^2]

A variable... represents a quantity's value that changes as a situation plays out A hose fills a swimming pool at a constant rate of 287 gallons/hour. Which explanation gives the fullest meaning of this value? Given a change in hours, (dt), the number of gallons added is (287)(dt). A hose fills a swimming pool at a constant rate of 287 gallons/hour. Symbols x, y, and m are defined for this situation in the conventional way. If x is defined as the total number of hours elapsed since th...

A summary of each unit of Calculus as it was presented to me. Helped to get my thoughts together and to summarize topics and write down important formulas!