Derivative Forms Memorize the following derivative forms. 1. d dx

math 251
(Bradford)
Derivative Forms
Memorize the following derivative forms.
d
dx
1.
2.
d
dx
3.
d
dx
4.
d
dx
5.
d
dx
sin u
= cos(u)
cos u
tan u
du
dx
du
= − sin(u)
dx
= sec2 (u)
du
dx
sec u
= sec(u) tan(u)
du
dx
7.
d
dx
d
dx
8.
d
dx
9.
u
n
u
= n un−1
= eu
e
cot u
du
dx
du
dx
= − csc2 (u)
du
dx
= − csc(u) cot(u)
csc u
du
dx
k
= 0
d
f (g(x)) = f 0 (g(x)) g 0 (x)
dx
Chain Rule
Product Rule
Sum/Difference Formula
d
dx
6.
d
dx
f (x) ± g(x)
0
d
dx
0
= f (x) ± g (x)
f (x) · g(x)
Constant Multiple Rule
Quotient Rule
d
dx
d
dx
k f (x)
0
= k f (x)
1
u(x)
v(x)
=
= f (x) · g 0 (x) + f 0 (x) · g(x)
v(x) · u0 (x) − u(x) · v0 (x)
[v(x)]2