Calculus Notes:
Definition of a Derivative:
definition 1:
lim
x a
f ( x)  f ( a)
xa
definition 2:
lim
h 0
f ( x  h)  f ( x )
h
Power Rule:
y  xn
y '  nx n1
Product Rule:
y  uv
y '  u ' v  uv ' … where u & v are both functions of x
Quotient Rule:
y
Chain Rule:
y  u(v)
u
v
Trig Functions:
y' 
u ' v  uv '
v2
… where u & v are both functions of x
y '  u '(v)  v ' … where u & v are both functions of x
Function
sinx
cosx
tanx
cscx
secx
cotx
Derivative
cosx
-sinx
sec2x
-cscxcotx
secxtanx
-csc2x
Natural Logarithm:
y  ln x
y'
1
x
Common Logarithm:
y  log a x
y' 
1
x ln a
Exponential Function:
y  ax
y '  a x ln a
Inverse Trig Functions:
Function
sin-1x
cos-1x
tan-1x
cot-1x
sec-1x
csc-1x
Derivative
1
√1 − x 2
1
−
√1 − x 2
1
1 + x2
1
−
1 + x2
1
|𝑥|√1 − x 2
−
1
|𝑥|√1 − x 2