Derivative Formulas:
Name: ________________________________
There will be a memory quiz over all these formulas before the chapter 4 unit test
y  uv
y  u ' v  u v'
1
" derivative of the first times the second, PLUS first times the derivative of the second"
u
u  v  u v
2
y
y
v2
v
"derivative of the top times the bottom, MINUS top times the derivative of the bottom,
“down dee-up MINUS up dee-down all over down down”
all divided by the bottom squared
For #3 - # 20: Assume that u is a function of x.
3
y  ku n
y   k n u ( n 1) u 
y  f (u )
dy dy du
4
y   f (u ) u  or

dx du dx
y  sin u
y   (cos u ) u 
5
y  cos u
y   (sin u ) u 
6
y  sec u
y   (sec u ) (tan u ) u 
7
y  csc u
y   (csc u ) (cot u ) u 
8
y  tan u
9
y   (sec u) 2 u 
10
y  cot u
11
y  eu
12
13
y  au
y  ln u
y   a u ( ln a) u 
1
u
y   u  or y  
u
u
14
y  sin 1 (u ) = inverse sine function
y 
15
y  cos 1 (u ) = inverse cosine function
16
y  tan 1 (u) = inverse tangent function
17
y  cot 1 (u) = inverse cotangent function
18
y  sec 1 (u) = inverse secant function
y   (csc u ) 2 u 
y  eu u
y 
1
1 u
1
1 u2
y  csc 1 (u) = inverse cosecant function
u  or y 
u or y  
u
1 u2
 u
1 u2
1
u
u or y  
2
1 u
1 u2
1
 u
y 
u or y  
2
1 u
1 u2
y 
1
y 
u
19
2
u 2 1
1
y 
u
u 2 1
u
u  or y  
u
u 2 1
 u
u
u 2 1
u  or y  
We will not learn about this formula until chapter 6 so it will not be on the memory quiz.
1
u
20
y  log b u
u  or
u ( ln b)
u ( ln b)