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### 37 Cards in this Set

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 definition of the derivative F'(x) = lim as h approaches 0 [f(x+h) - f(x)] / h derivative of a constant times a function d/dx (k(u(x))) = k du/dx Power Rule (variable raised to a constant) d/dx (u^n) = nu^(n-1) du/dx The Sum Rule d/dx (u+v) = du/dx + dv/dx The Difference Rule d/dx (u-v) = du/dx - dv/dx The Product Rule d/dx (uv) = uv' + vu' The Quotient Rule d/dx (u/v) = [vu' - uv'] / v^2 The Chain Rule dy/dx = dy/du * du/dx or d/dx (f(g(x)) = f'(g(x))g'(x) The Derivative of the Sine d/dx (sinu) = cosu du/dx The Derivative of the Cosine d/dx (cosu) = -sinu du/dx The Derivative of the Tangent d/dx (tanu) = sec^2 u du/dx The Derivative of the Cotangent d/dx (cotu) = -csc^2 u The Derivative of the Secant d/dx (secu) = secu tanu du/dx The Derivative of the Cosecant d/dx (cscu) = -cscu cotu du/dx The Derivative of the Inverse Sine d/dx (Sin^-1 u) = 1/sqrt(1-u^2) du/dx The Derivative of the Inverse Cosine d/dx(Cos^-1 u) = -1/sqrt(1-u^2) du/dx The Derivative of the Inverse Tangent d/dx(Tan^-1 u) = 1/(1+u^2) du/dx The Derivative of the Inverse Cotangent d/dx(Cot^-1 u) = -1/(1+u^2) du/dx The Derivative of the Inverse Secant d/dx(Sec^-1 u) = 1/(|u|sqrt(u^2 - 1) du/dx The Derivative of the Inverse Cosecant d/dx(Csc^-1 u) = -1/(|u|sqrt(u^2 - 1) du/dx The Derivative of the Natural Log d/dx (ln u) = 1/u du/dx The Derivative of the log to base a d/dx (loga u) = 1/(u lna) du/dx The Derivative of e raised to a variable d/dx (e^u) = e^u du/dx The Derivative of a constant raised to a variable d/dx (a^u) = a^u lna du/dx Pythagorean Identities sin^2 x + cos^2 x = 1 tan^2 x +1 = sec^2 x 1 + cot^2 x = csc^2 x sin even/odd formula sin (-x) = -sinx cos even/odd formula cos(-x) = cosx tan even/odd formula tan(-x) = -tanx csc even/odd formula csc(-x) = -cscx sec even/odd formula sec(-x) = secx cot even/odd formula cot(-x) = -cotx double angle formula: sin(2x) = 2sinx cosx double angle formula: cos(2x) = cos^2 x - sin^2 x = 2cos^2 x - 1 = 1-2sin^2 x half angle formula: cos^2 x = (1/2)(1+cos(2x)) double angle formula: tan(2x) = (2tanx)/(1-tan^2 x) half angle formula: sin^2 x = (1/2)(1-cos(2x)) half angle formula: tan^2 x = (1-cos(2x))/(1+cos(2x))