MAC-2311 Study Guide - Midterm Guide: Implicit Function, Inverse Trigonometric Functions, Minute And Second Of Arc
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Periodicity of derivatives of sin x and cos x. If f(x) = sin x: f (x) = cos x f "(x) = -sin x f ""(x) = -cos x f (4)(x) = sin x. If f(x) = cos x: f (x) = -sin x f "(x) = -cos x f ""(x) = sin x f (4) (x) = cos x. 3. 4: the chain rule d/dx (f(g(x))) = f (g(x)) x g (x) General power rule: d/dx (g(x))n = n(g(x))n-1 x g (x) Used when you have a formula that cannot be solved for y; you do implicit differentiation and solve for dy/dx. Derivatives of inverse trig functions d/dx (arcos x) = -1/ (1-x2) d/dx (arctan x) = 1/(1+x2) d/dx (arccot x) = -1/(1+x2) d/dx (arcsin x) = 1/ (1-x2) d/dx (arcsec x) = 1/x (x2-1) d/dx (arccsc x) = -1/x (x2-1) Logarithmic differentiation: use log rules to simplify a complicated derivative (remember to plug y back into the equation).
