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Complete Derivatives
Basics in Calculus
Question | Answer |
---|---|
x | 1 |
C | 0 |
CU | CU' |
U^n | nU^(n-1)U' |
f(g(x)) | f'(g(x))g'(x) |
U+V | U'+V' |
UV | U'V+UV' |
U/V | U'V-UV'/V^2 |
|U| | (U/|U|)U' |
e^u | e^u u' |
a^u | lna a^u u' |
lnu | (1/u) u' |
logaU | (1/lna)(1/U)U' |
sinx | cosx x' |
cosx | -sinx x' |
tanx | sec^2x x' |
cscx | -cscxcotx x' |
secx | secxtanx x' |
cotx | -csc^2x x' |
arcsinx | (x')/squareroot[1-x^2] |
arccosx | (-x')/squareroot[1-x^2] |
arctanx | x'/(1+x^2) |
arccscx | (-x')/|x|squareroot[1-x^2] |
arcsecx | (x')/|x|squareroot[1-x^2] |
arccotx | -x'/(1+x^2) |