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33 Cards in this Set

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 derive ln(x) 1/tdt so integral of 1/t dt = ln(x) ln 1 = 0 ln(ab)= ln a + ln b ln (a ^n) n ln(a) ln(a/b) ln(a)-ln(b) e is? the base for natural log ln e = 1 also, integral 1/t dt from 1 to e derive nat log: ln(u) 1/u*(du/dx) only include the du dx if the u is a chain rule and not just an x d/dx of ln abs(u) u'/u integral 1/x ln abs (x) integrate (1/u) ln abs(u) + c integral sin u -cos u +c integral cos u sin u + c integral tan u ln abs(sin u ) + c inverse of the natural log is the natural exponential function, f^-1(x)=e^x e^a*e^b= e^a+b e^a/e^b e^a-b d/dx e^u e^u*(du/dx) only include the du/dx if the u is a chain rule, if not the e^x derives to itself. integral of e^u du e^u+c a^x= (ln a)*a^x loga(x)= log base a of x 1/(ln a)*(ln x) d/dx (a^u)= (ln a)*a^u *du/dx d/dx (log a u) derivative, log base a of u 1/((ln a)u) * du/dx only additional multiply for du/dx if its a chain rule d/dx u^n n*u^(n-1) * du/dx only additional multiply for du/dx if its a chain rule inverse trig functions: input/output ? input ratio and output angle accoridn gto the formula sheet, the what are the formulas of the functions not given : arcsin -> arctan -> arcsec -> arccos arccot arccsc all now include a negative u' on top. exponential growth and decay model y=Ce^kt d/dx ln(u) u'/u ln(0) undefined e^1 e cos(0) 1 sin(0) 0 e^0 1