Mathematics reference
Rules for differentiation
 18Ma5 MathRef
Essential rules for differentiation.

Legend.
• a and n are constants,
• u and v are functions of x,
• d is the differential operator.
Basic.
(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] equation 35
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