DERIVATIVE FORMULAS
A. Algebraic Functions
1.
2.
3.
4.
5.
6.
7.
8.
dc
dx
d
dx
d
dx
d
dx
d
dx
d
dx
=0
(u + v) =
(uv) = u
v
u
(v ) =
du
dx
dv
dx
d
u
+v
dv
dx
du
dx
du
dv
−u
dx
dx
v2
un = nun−1
√u =
+
du
dx
du
dx
2√u
1 du
( ) = c dx
dx c
d c
dx u
=
du
dx
u2
c
B. Exponential Functions
9.
d
dx
10.
(au ) = au In a
d
dx
(eu ) = eu
du
dx
du
dx
C. Logarithmic Functions
11.
12.
13.
d
dx
d
dx
d
dx
(log a u) =
(log10 u) =
(In u) =
loga e
du
dx
u
log10 e
du
dx
u
du
dx
u
D. Trigonometric Functions
14.
15.
16.
17.
18.
19.
d
dx
d
dx
d
dx
d
dx
d
dx
d
dx
(sin u) = cos u
du
dx
(cos u) = −sin u
(tan u) = sec 2 u
du
dx
du
dx
(cot u) = −csc 2 u
du
dx
(sec u) = sec u tan u
du
dx
(csc u) = −csc u cot u
du
dx
E. Inverse Trigonometric Functions
20.
21.
22.
23.
d
dx
d
dx
d
dx
d
dx
(sin−1 u) =
(cos −1 u) =
(tan−1 u) =
(cot −1 u) =
1
du
√1−u2 dx
1
du
√1−u2
dx
1
du
1+u2
dx
−1
du
1+u2
dx
24.
25.
d
dx
d
dx
(sec −1 u) =
(csc −1 u) =
1
du
u√u2 −1
dx
−1
du
u√u2 −1
dx
F. Hyperbolic Functions
26.
27.
28.
29.
30.
31.
d
dx
d
dx
d
dx
d
dx
d
dx
d
dx
(sinh u) = cosh u
(cosh u) = sinh u
du
dx
du
dx
(tanh u) = sec h2 u
du
dx
(coth u) = −csc h2 u
du
dx
(sec hu) = −sec hu tanh u
(csc hu) = −csc hu coth u
du
dx
du
dx