Formulas:
d
f (x + h) − f (x)
[f (x)] = f 0 (x) = lim
h→0
dx
h
d x
[e ] = ex
dx
d
[ln |x|] = 1/x, x 6= 0
dx
d
[f (x)g(x)] = f 0 (x)g(x) + g 0 (x)f (x)
dx
d
[f (g(x))] = f 0 (g(x))g 0 (x)
dx
R
f (x) dx = F (x) + C, if F 0 (x) = f (x)
d r
[x ] = rxr−1
dx
ax = ex ln(a)
ln(x)
loga (x) =
ln(a)
d f (x)
f 0 (x)g(x) − g 0 (x)f (x)
=
dx g(x)
[g(x)]2
d
dy du
[f (g(x))] =
·
, where y = f (u), u = g(x)
dx
du dx
Rb
f (x) dx = F (b) − F (a), if F 0 (x) = f (x)
a