| f(x) | f'(x) | f''(x) |
|---|---|---|
| y = sin(x) | y = cos(x) | y = -sin(x) |
| y = cos(x) | y = -sin(x) | y = -cos(x) |
| y = tan(x) | y = sec2(x) | y = 2 tan(x)/cos2(x) |
| y = sin-1(x) | y = 1/√1 - x2 | y = x/√(1 - x2)3 |
| y = cos-1(x) | y = -1/√1 - x2 | y = -x/√(1 - x2)3 |
| y = tan-1(x) | y = 1/(x2 + 1) | y = -2x/(x2 + 1)2 |
| y = csc(x) | y = -csc(x) cot(x) | y = 2 cot2(x) + 1/sin(x) |
| y = sec(x) | y = sec(x) tan(x) | y = 2 tan2(x) + 1/cos(x) |
| y = cot(x) | y = -csc2(x) | y = 2 cot(x)/sin2(x) |
| y = ex | y = ex | y = ex |
| y = x2 | y = 2x | y = 2 |
| y = x3 | y = 3x2 | y = 6x |
| y = x ln x - x | y = ln x | y = 1/x |
| y = ln x | y = 1/x | y = -1/x2 |
See a visualization to show why the derivative of ex is ex.