click below
click below
Normal Size Small Size show me how
calculus mem sheet
Term | Definition |
---|---|
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)) |