DERIVATE
Derivate fondamentali
α ∈ R ; a > 0 ∧ a 6= 1
f (x)
f 0 (x)
c
0
xα
√
x
α · xα−1
1
√
2 x
ax
ax · ln a
ex
ex
loga x
ln x
1
· loga e
x
1
x
sen x
cos x
cos x
− sen x
1
cos2 x
1
arcsen x √
1 − x2
1
arccos x − √
1 − x2
1
arctg x
1 + x2
Algebra delle derivate
y
y0
f (x) + g(x)
f 0 (x) + g 0 (x)
f (x) · g(x)
f 0 (x) · g(x) + f (x) · g 0 (x)
c · f (x)
c · f 0 (x)
f (x)
g(x)
f 0 (x) · g(x) − f (x) · g 0 (x)
[g(x)]2
1
g(x)
−
g 0 (x)
[g(x)]2
tg x
f (g(x))
f 0 (z) · g 0 (x) | z=g(x)
