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### 20 Cards in this Set

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 definition of a derivative lim f(x+h)-f(x) h->0 h power rule d/dx x^r= rx^(r-1) how can a derivative NOT exist 1) discontinuities (jump, hole) 2) kink/sharp edge 3) vertical tangent (x^1/3 at x=0) sums of derivatives d/dx( (f(x) + g(x) ) = d/dx f(x) + d/dx g(x) product rule: f'(x)g(x) + g'(x)f(x) quotient rule d/dx f(x)/g(x)= g(x)f'(x)- (f(x)g'(x)) g(x)^2 d/dx sinx cosx d/dx cosx -sinx d/dxtanx sec^2x or 1/cos^2x d/dx secx secxtanx d/dx cscx -cscxcotx d/dx cotx -csc^2x d/dx a^x loga(a^x) *****log is BASE e d/dx log x a (1/loga)(1/x) d/dx logx 1/x d/dx e^x e^x d/dx sin^-1x 1/√(1-x^2) d/dx cos^-1x -1/√(1-x^2) d/dx tan^-1x 1/1-x^2 chain rule: d/dx g(f(x))= g'(f(x)) * f'(x)