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Derivative Table
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Derivative Table
Most common function's derivative...
Author:
Raabin Tjedmankic
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Tabella delle derivate e delle primitive fondamentali F (x) =
f (x) dx
1
n−
x
nx
n
||
e
√ x
m
√ n m x √ −n m
√ 1x
m
m
n
∈ (−∞, 0) oppure x ∈ (0, +∞) n, m ∈ N e m ≥ 2, x < 0 x > 0 n, m
+n
x
m
1
αx
α
e
x
α
x
e
a
1
||
1 log e =x
x log a
em
≥ 2, x < 0
o
x > 0
∈ R, x > 0
a > 0, a = 1, x > 0 oppure x < 0
a
e
sin x
cos x
cos x
− sin x
tang x
1 + tang2 x =
cotang x
−1 − cotang
arcsin x
1
2
1 cos2 x x =
1 sin2 x
−
2
1
−x −1 1−x
arccos x
2
arctan x
1 1 + x2
arccotan x
1 1 + x2
−
sinh x
cosh x
cosh x
sinh x 2
tanh x
1
− tanh
cotanh x
1
− cotanh
settsinh x
1
2
1 cosh2 x
x =
1 sinh2 x
−
x > 1
−
setttanh x
−1 < x < 1
−
settcotanh x
1 log 1 + x 2 1 x
−
x =
1 + x2 1 x2 1 1 1 x2
settcosh x
+
a > 0
x
log x
∈N
x
a log a
a
o
+
m−n
α−
x
∈N
x
x
n
m
n
1
log x
e
f (x) = F (x)
1
2
(x <
−1) oppure (x > 1)
2
(x <
−1) ( −1 < x < 1)
1
−x
1
−x
1
1
o
( x > 1)
o
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