MATH 30.23_Module 1 & 2: Limits & Derivatives

lim (x→0) (sin x)/x

1

lim (x→0) (cos x - 1)/x

0

d/dx sin x

cos x

d/dx cos x

-sin

d/dx tan x

= sec² x

= 1/cos² x

d/dx csc x

-csc x • cot x

d/dx sec x

sec x • tan x

d/dx cot x

- csc² x

d/dx sin x • cos x

= cos 2x

= cos² x - sin² x

d/dx e^u

e^u • u’

d/dx x^e

ex^e-1

d/dx e²

0

d/dx a^x

a^x • x’ • ln a

d/dx ln x

x’/x

d/dx log_a(u)

u’/(u • ln a)

ln (x)²

2 • ln x

cos θ

x

sin θ

y

tan θ

= sin θ / cos θ

= y / x

cot θ

= 1 / tan θ

= cos θ / sin θ

= x / y

csc θ

1 / sin θ

sec θ

1 / cos θ

sin² x + cos² x

1

1 + cot² x

csc² x

tan² x + 1

sec² x