Download Calculus and Trigonometry Formula Sheet

A Few Important Formulas
1. Derivative Rules
(a) [f (x)g(x)]0 = f 0 (x)g(x) + f (x)g 0 (x) (product rule)
0
f (x)
f 0 (x)g(x) − f (x)g 0 (x)
(b)
=
(quotient rule)
g(x)
[g(x)]2
(c) [f (g(x))]0 = f 0 (g(x))g 0 (x) (chain rule)
2. Integration Formulas
Z
(a)
A dx = Ax + C
Z
1
(b)
eax dx = eax + C
a
Z
xn+1
+ C if n 6= −1
(c)
xn dx =
n+1
Z
1
(d)
dx = ln |x| + C
x
Z
ln |ax + b|
1
(e)
dx =
+C
ax + b
a
Z
(f)
sin x dx = − cos x + C
Z
(g)
cos x dx = sin x + C
Z
(h)
sec2 x dx = tan x + C
Z
(i)
csc2 x dx = − cot x + C
Z
(j)
sec x tan x dx = sec x + C
Z
(k)
csc x cot x dx = − csc x + C
Z
1
1
(l)
dx = arctan x + C
2
2
a +b
a
Z
Z
(m)
u dv = uv − v du (integration by parts)
3. Trigonometric Formulas
(a) sin2 x + cos2 x = 1
1
(b) 1 + tan2 x = sec2 x
(c) 1 + cot2 x = csc2 x
(d) sin (2x) = 2 sin x cos x
(e) cos (2x) = 2 cos2 x − 1 = 1 − 2 sin2 x = cos2 x − sin2 x
2