(d/dx) (a u) = a du/dx | equation 1 |
(d/dx) (u +- v) = du/dx +- dv/dx | equation 2 |
(d/dx) (u v) = u dv/dx + du/dx v | equation 3 |
(d/dx) (u/v) = (v du/dx - u dv/dx)/v2 | equation 4 |
(d/dx) a = 0 | equation 5 |
(d/dx) x = 1 | equation 6 |
(d/dx) xn = n xn - 1 | equation 7 |
(d/dx) x1/2 = (1/2) x-1/2 | equation 8 |
(d/dx) |x| = x/|x|, x != 0 | equation 9 |
(d/dx) ex = ex | equation 10 |
(d/dx) ln x = 1/x | equation 11 |
Trigonometry. | |
(d/dx) sin x = cos x | equation 12 |
(d/dx) cos x = -sin x | equation 13 |
(d/dx) tan x = sec2 x | equation 14 |
(d/dx) cot x = -csc2 x | equation 15 |
(d/dx) sec x = sec x tan x | equation 16 |
(d/dx) csc x = -csc x cot x | equation 17 |
(d/dx) arcsin x = 1/(1 - x2)1/2 | equation 18 |
(d/dx) arccos x = -1/(1 - x2)1/2 | equation 19 |
(d/dx) arctan x = 1/(1 + x2) | equation 20 |
(d/dx) arccot x = -1/(1 + x2) | equation 21 |
(d/dx) arcsec x = 1/[|x| (x2 - 1)1/2] | equation 22 |
(d/dx) arccsc x = -1/[|x| (x2 - 1)1/2] | equation 23 |
Hyperbolic trigonometry. | |
(d/dx) sinh x = cosh x | equation 24 |
(d/dx) cosh x = sinh x | equation 25 |
(d/dx) tanh x = sech2 x | equation 26 |
(d/dx) coth x = -csch2 x | equation 27 |
(d/dx) sech x = -sech x tanh x | equation 28 |
(d/dx) csch x = -csch x coth x | equation 29 |
(d/dx) arcsinh x = 1/(x2 + 1)1/2 | equation 30 |
(d/dx) arccosh x = 1/(x2 - 1)1/2 | equation 31 |
(d/dx) arctanh x = 1/(1 - x2) | equation 32 |
(d/dx) arccoth x = 1/(1 - x2) | equation 33 |
(d/dx) arcsech x = -1/[x (1 - x2)1/2] | equation 34 |
(d/dx) arccsch x = -1/[|x| (1 + x2)1/2] |
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