Tabella delle derivate e delle primitive fondamentali
F (x) =R
f (x) dx f (x) = F0(x)
xn nxn−1 n ∈ N
loge|x| 1
x x ∈ (−∞, 0) oppure x ∈ (0, +∞)
m√
xn n
mm√
xm−n n, m ∈ N+ e m ≥ 2, x < 0 o x > 0 1
m√ xn
−n mm√
xm+n n, m ∈ N+ e m ≥ 2, x < 0 o x > 0
xα αxα−1 α ∈ R, x > 0
ex ex
ax axlogea a > 0
loga|x| 1
x logea = 1
x logae a > 0, a 6= 1, x > 0 oppure x < 0
sin x cos x
cos x − sin x
tang x 1 + tang2x = 1
cos2x cotang x −1 − cotang2x = −1
sin2x
arcsin x p 1
1 − x2
arccos x p−1
1 − x2
arctan x 1
1 + x2
arccotan x −1
1 + x2
sinh x cosh x
cosh x sinh x
tanh x 1 − tanh2x = 1
cosh2x cotanh x 1 − cotanh2x = −1 sinh2x
settsinh x p 1
1 + x2
settcosh x p 1
x2− 1 x > 1
setttanh x 1
1 − x2 −1 < x < 1
settcotanh x 1
1 − x2 (x < −1) oppure (x > 1) 12 log
¯¯
¯ 1 + x1 − x
¯¯
¯ 1
1 − x2 (x < −1) o (−1 < x < 1) o (x > 1)
1
