Table of Derivatives
Below is a table of derivatives we should be familiar with.
0
f
f
cf
cf 0
0
f ±g
f ± g0
fg
f 0g + f g0
f (g(x)) f 0 (g(x))g 0 (x)
f
g
f 0 g−f g 0
g2
f (x)g(x)
Use log diff.
f
f0
c
0
n
x
nxn−1
x
e
ex
ax ax ln(a)
1
ln |x|
x
f
f0
sin(x)
cos(x)
cos(x)
− sin(x)
sec2 (x)
tan(x)
sec(x)
sec(x) tan(x)
csc(x) − csc(x) cot(x)
cot(x)
− csc2 (x)
√ 1
sin−1 (x)
1−x2
1
tan−1 (x)
1+x2
Table of Antiderivatives
Below is a table of antiderivatives that we get by taking the derivative table and swapping
columns. The arbitrary constant has been left off to save space.
f
F
cf
cF
f ±g F ±G
f
c
xn
1/x
ex
F
cx
1
xn+1
n+1
ln |x|
ex
In Class Example
1
f
F
cos(x)
sin(x)
sin(x)
− cos(x)
sec2 (x)
tan(x)
sec(x) tan(x) sec(x)
√ 1
sin−1 (x)
1−x2
1
tan−1 (x)
1+x2