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Derivative Formulas
Rules of Derivatives and Derivative of Trigonometric and Hyperbolic Functions
| Question | Answer |
|---|---|
| c | 0 |
| au^n | nau^(n-1) du/dx |
| sin(u) | cos(u) du/dx |
| cos(u) | -sin(u) du/dx |
| tan(u) | sec^2(u) du/dx |
| cot(u) | -csc^2(u) du/dx |
| sec(u) | sec(u)tan(u) du/dx |
| csc(u) | -csc(u)cot(u) du/dx |
| arcsin(u) | 1/sqrt(1 - u^2) du/dx |
| arccos(u) | -1/sqrt(1-u^2) du/dx |
| arctan(u) | 1/(1+u^2) du/dx |
| arccot() | -1/(1+u^2) du/dx |
| arcsec(u) | 1/(|u|sqrt(u^2 - 1)) du/dx |
| arccsc(u) | -1/(|u|sqrt(u^2 - 1) )du/dx |
| a^u | a^uln(a) du/dx |
| e^u | e^u du/dx |
| log a(u) | 1/uln(a) du/dx |
| ln(u) | 1/u du/dx |
| sinh(u) | cosh(u) du/dx |
| cosh(u) | sinh(u) du/dx |
| tanh(u) | sech^2(u) du/dx |
| coth(u) | -csch^2(u) du/dx |
| sech(u) | -sech(u)tanh(u) du/dx |
| csch(u) | -csch(u)coth(u) du/dx |
| arcsinh(u) | 1/sqrt(1 + u^2) du/dx |
| arccosh(u) | 1/sqrt(u^2 - 1) du/dx, u > 1 |
| arctanh(u) | 1/(1 - u^2) du/dx, |u| < 1 |
| arccoth(u) | 1/(1-u^2) du/dx, |u| > 1 |
| arcsech(u) | -1/usqrt(1 - u^2) du/dx, 0 < u < 1 |
| arccsch(u) | -1/|u|sqrt(1 + u^2) du/dx, u =/= 0 |
Created by:
jefranco1
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