L'Hopitals Rule - assume f and g are differentiable functions on an open interval (a,b) containing c, and that g'(x)=/ 0. for all x in (a,b) except possibly at c itself. Then if lim x-> c f(x) = g , then lim x->c f(x)/g(x)= lim x->c f'(x)/g'(x), Distance Traveled - the sum of the absolute values of the distances between turning points, Displacement over an interval [a,b] - s(b)-s(a) is the difference in distance from start to stop, Speed - the rate at which the position is changing, |velocity|=|v(t)|= ds/dt, Derivatives of Trig Functions - d/dx cos x = -sin x | d/dx sin x = cos x | d/dx tan x = sec^2x | d/dx csc x = -cscxcotx | d/dx sec x = secxtanx | d/dx cotx = -csc^2 x |, Derivatives of Inverse Functions - let f(x) and g(x) be inverse functions then g'(x) = 1/(f'(g(x)) , Derivatives of Inverse Trig Functions - d/dx sin ^-1(x) = 1/square root of (1-x^2) | d/dx tan^-1(x) = 1/1+x^2 | d/dx sec^-1(x) = 1/(|x|square root of (x^2-1),

Applications of Derivatives AP CALC AB Definitions

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