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# calculus mem sheet

TermDefinition
d/dx[ku] k(du/dx)
d/dx[k] 0
d/dx[uv] u(dv/dx)+v(du/dx)
d/dx[u/v] (v(du/dx)-u(dv/dx))/v^2`
d/dx[e^u] (e^u)(du/dx)
d/dx[ln u] (1/u)(du/dx)
d/dx[sin u] (cos u)(du/dx)
d/dx[cos u] (-sin u)(du/dx)
d/dx[tan u] (sec^2 u)(du/dx)
d/dx[cot u] (-csc^2 u)(du/dx)
d/dx[sec u] (sec u)(tan u)(du/dx)
d/dx[csc u] (-csc u)(cot u)(du/dx)
d/dx[sin^-1 u] (1/((1-u^2)^1/2)(du/dx) or (1/squareroot(1-u^2))(du/dx)
d/dx[tan^-1 u] (1/(1+u^2))/(du/dx)
d/dx[sec^-1 u) (1/(|u|)((u^2 -1)^1/2))(du/dx)
int(kdu) ku+C
int((u^n)(du)) ((u^n+1)/(n+1))+C
int(du/u) ln|u|+C
int((e^u)(du)) e^u+C
int((sin u)(du)) (-cos u)+C
int((cos u)(du)) (sin u)+C
int((tan u)(du)) (-ln|cos u|)+C
int((cot u)(du)) (ln|sin u|)+C
int((sec u)(du)) (ln|sec u + tan u|)+C
int((csc u)(du)) (-ln|csc u + tan u|)+C
int((sec^2 u)(du)) (tan u)+C
int((csc^2 u)(du)) (-cot u)+C
int((sec u)(tan u)(du)) (sec u)+C
int((csc u)(cot u)(du)) (-csc u)+C
int((du/((a^2-u^2)^1/2)) (sin^-1 |u|/a)+C
int((du/(a^2+u^2))(du)) (1/a)(tan^-1 u/a)+C
int((du/(u((u^2-a^2)^1/2)))) (1/a)(sec^-1 u/a)+C
d/dx[f^-1(x)] 1/(f')(f^-1(x))
Created by: mrteddy6564