Common Derivatives & Differentiation Rules Flashcards

1

d/dx sin(x)

sin(x)+xcos(x)
1/csc(x)
cos(x)
-cos(x)

2

d/dx ln(f(x))

f'(x)/f"(x)
f'(x)/f(x)
f'(x)⋅ln(f(x))
f'(x)/ln(f(x))

3

d/dx cot(x)

-sec2(x)
-csc2(x)
-csc(x)
csc2(x)

4

d/dx ln(x)

1/x2
1/x
1/ln(x)
x/1

5

Quotient Rule [d/dx f(x)/g(x)]

(f'(x)⋅g(x)-g'(x)⋅f(x))/[g(x)]2
(f'⋅g-g'⋅f)/(g2)
(f'(x)⋅g(x)+g'(x)⋅f(x))/[g(x)]2
(f'⋅g+g'⋅f)/(g2)

6

Power Rule xⁿ

(n-1)⋅xn
(n-1)⋅xn+1
xn-1
n⋅xn-1

7

d/dx e^g(x)

eg'(x)
g"(x)eg'(x)
g'(x)eg(x)
g(x)eg'(x)

8

Chain Rule (d/dx [f(x)]ⁿ)

n[f(x)]n-1⋅f'(x)
(n-1)⋅[f(x)]n-1⋅f'(x)
n[f(x)]n+1⋅f'(x)
n[f'(x)]n-1⋅f"(x)

9

d/dx csc(x)

csc(x)-xcsc(x)cot(x)
csc(x)tan(x)
-sec(x)tan(x)
-csc(x)cot(x)

10

d/dx sec(x)

tan2(x)
-sec(x)tan(x)
sec(x)tan(x)
-csc(x)cot(x)

11

d/dx C C is any constant

C-1
C
C+1
0

12

d/dx tan(x)

csc2(x)
sin(x)/cos(x)
tan2(x)
sec2(x)

13

d/dx (cx)

c'x+x'c
x
cx'
c

14

d/dx cos(x)

-1/sec(x)
sin(x)
-sin(x)
tan(x)

15

Product Rule [d/dx f(x)⋅g(x)]

f'(x)⋅g(x)+g'(x)⋅f(x)
f'(x)⋅g'(x)+f"(x)⋅g"(x)
f'⋅g+g'⋅f
f(x)⋅g(x)+f'(x)⋅g'(x)

16

d/dx e^x

xex
ex
ln(ex)
1/ex

Common Derivatives & Differentiation Rules

Questions 16

Common Derivatives & Differentiation Rules

Questions 16