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AP Calculus Flashcards

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6583172349d/dx (x^2)2x0
6583172350d/dx (sin x)cos x1
6583172351d/dx (cos x)-sin x2
6583172352d/dx (tan x)(sec x)^23
6583172353d/dx (cot x)-(csc x)^24
6583172354d/dx (sec x)(sec x)(tan x)5
6583172355d/dx (csc x)-(csc x)(cot x)6
6583172356d/dx (e^x)e^x7
6583172357d/dx (ln x)1/x8
6583172358Log A + Log BLog (AB)9
6583172359Log A - Log BLog (A/B)10
6583172360k Log ALog (A^k)11
6583172361Point-slope form of a liney-y1 = m (x-x1)12
6583172362Product ruled/dx (uv) = uv' + vu'13
6583172363Quotient ruled/dx (u/v) = (vu'-uv')/(v^2)14
6583172364Rolle's TheoremLet f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval).15
6583172365Mean Value TheoremIf f is continuous on [a,b] and differentiable on (a,b), then there exists a number c on (a,b) such that f'(c)=(f(b)-f(a))/(b-a)16
6583172366d/dx (b^x)b^x (ln b)17
6583172367d/dx (log to the base b of x)1 / (x ln b)18
6583172368d/dx (x^3)3x^219

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