derivate fondamentali .pdf
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Tabella delle derivate e delle primitive fondamentali
F (x) =
R
f (x) dx
f (x) = F 0 (x)
xn
nxn−1
n∈N
loge |x|
1
x
x ∈ (−∞, 0) oppure x ∈ (0, +∞)
√
√n
xm−n
√−n
m
m xm+n
n, m ∈ N+ e m ≥ 2, x < 0 o x > 0
xα
αxα−1
α ∈ R, x > 0
ex
ex
ax
ax loge a
a>0
loga |x|
1
1 log e
=x
a
x loge a
a > 0, a 6= 1, x > 0 oppure x < 0
sin x
cos x
cos x
− sin x
tang x
1 + tang2 x =
cotang x
−1 − cotang2 x = −1
sin2 x
arcsin x
p 1
1 − x2
p −1
1 − x2
1
1 + x2
m
xn
√1
xn
m
arccos x
arctan x
m
m
n, m ∈ N+ e m ≥ 2, x < 0 o x > 0
1
cos2 x
arccotan x
−1
1 + x2
sinh x
cosh x
cosh x
sinh x
tanh x
1 − tanh2 x =
cotanh x
1 − cotanh2 x =
settsinh x
p 1
1 + x2
p 1
x2 − 1
1
1 − x2
x>1
1
1 − x2
(x < −1) oppure (x > 1)
1
1 − x2
(x < −1) o (−1 < x < 1) o (x > 1)
settcosh x
setttanh x
settcotanh x
¯
¯
1 log ¯¯ 1 + x ¯¯
2
1−x
1
cosh2 x
−1
sinh2 x
−1 < x < 1
1

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