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### 47 Cards in this Set

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 d/dx[cu] cu' d/dx[u +/- v] u' +/- v' d/dx[uv] uv' + vu' d/dx[u/v] (vu' - uv')/v^2 d/dx[c] 0 d/dx[u^n] nu^(n-1) u' d/dx[x] 1 d/dx[|u|] (u/|u|)*(u'), u ≠ 0 d/dx[ln u] u'/u d/dx[e^u] e^u*u' d/dx[log base a of u] u'/((ln a)* u) d/dx[a^u] (ln a)*a^u*u' d/dx[sin u] (cos u) u' d/dx[cos u] -(sin u) u' d/dx[tan u] (sec^2 u) u' d/dx[cot u] -(csc^2 u) u' d/dx[sec u] (sec u tan u) u' d/dx[csc u] -(csc u cot u) u' d/dx[arcsin u] u'/(sqrt(1-u^2)) d/dx[arccos u] -u'/(sqrt(1-u^2)) d/dx[arctan u] u'/(1+u^2) d/dx[arccot u] -u'/(1+u^2) d/dx[arcsec u] u'/(|u| sqrt(u^2-1)) d/dx[arccsc u] -u'/(|u| sqrt(u^2-1)) ⨛kf(u)du k⨛f(u)du ⨛[f(u) +/- g(u)] du ⨛f(u) du +- ⨛g(u) du ⨛du u+c ⨛u^n du ((u^(n+1))/(n+1)) + c, n ≠ -1 ⨛du/u ln|u|+c ⨛e^u du e^u + c ⨛a^u du (1/ln a) a^u + c ⨛sin u du -cos u + c ⨛cos u du sin u + c ⨛tan u du -ln|cos u| + c ⨛cot u du ln|sin u| + c ⨛sec u du ln|sec u + tan u| + c ⨛csc u du -ln|csc u + cot u| + c ⨛sec^2 u du tan u + c ⨛csc^2 u du -cot u + c ⨛sec u tan u du sec u + c ⨛csc u cot u du -csc u + c ⨛du/(sqrt( a^2 - u^2)) arcsin (u/a) + c ⨛du/(a^2 + u^2) (1/a) arctan (u/a) + c ⨛du/(u(sqrt( u^2 - a^2))) (1/a) arcsec (|u|/a) + c sin^2 u + cos^2 u 1 1 + tan^2 u sec^2 u 1 + cot^2 u csc^2 u