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### How to study your flashcards.

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### 45 Cards in this Set

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 d/dx [C] 0 d/dx [kx] k d/dx [k f(x)] k f'(x) d/dx [f(x) +- g(x)] f'(x) +- g'(x) d/dx [x^n] nx^(n-1) d/dx [sinx] cosx d/dx [cosx] -sinx d/dx [tanx] sec²x d/dx [secx] secxtanx d/dx [cotx] -csc²x d/dx [cscx] -cscxcotx \$ 0dx C \$ kdx kx + C \$ kf(x)dx k \$f(x)dx \$ [f(x) +- g(x)] \$f(x) + \$g(x) \$ x^ndx (x^(n+1))/(n+1) + C \$ cosxdx sinx + C \$ sinxdx -cosx + C \$ sec²x tanx + C \$ secxtanx secx + C \$ csc²x -cotx + C \$ cscxcotxdx -cscx + C d/dx [ln x] 1/x d/dx [ln u] 1/u du d/dx [ln |u|] 1/u du d/dx [e^x] e^x d/dx [e^u] e^u du d/dx [e^e] o d/dx [x^e] ex^(e-1) d/dx [a^x] (ln a)a^x d/dx [a^u] (ln a)a^u du d/dx [loga x] 1/((ln a)x) d/dx [loga u] 1/((ln a)u) \$ 1/x dx ln |x| + C \$ 1/u du ln |u| + C \$ e^x dx e^x + C \$ e^u du e^u + C \$ a^x dx (1/(ln a))a^x + C \$ sinu du -cosu + C \$ cosu du sinu + C \$ tanu du -ln |cos u| + C \$ cotu du ln |sin u| + C \$ secu du ln |secu + tanu| + C \$ cscu du -ln |cscu + cotu| + C When should you use long division? When the degree of the numerator is equal to or larger than the degree of the denominator