Basic Diffentiation Rules

Question 1

d/dx[cu] = ?

Answer 1

cu’

Question 2

d/dx[u ± v] = ?

Answer 2

u’ ± v’

Question 3

d/dx[fg] = ?

Answer 3

fg’ + gf’

Question 4

d/dx[f/g] = ?

Answer 4

gf’ - fg’

g^2

Question 5

d/dx[c] = ?

Answer 5

0

Question 6

d/dx[xⁿ] = ?

Answer 6

nx^n-1

Question 7

d/dx[x] = ?

Answer 7

1

Question 8

d/dx[sin x] = ?

Answer 8

cos x

or

(cos x) * x’

Question 9

d/dx[cos x] = ?

Answer 9

-sin x

or

-(sin x) * x’

Question 10

d/dx[tan x] = ?

Answer 10

sec² x

or

(sec² x) * x’

Question 11

d/dx[cot x] = ?

Answer 11

-csc² x

or

-(csc² x) * x’

Question 12

d/dx[sec x] = ?

Answer 12

sec x tan x

or (sec x tan x) * x’

Question 13

d/dx[csc x] = ?

Answer 13

-csc x cot x

or

-(csc x cot x) * x’

Question 14

d/dx[f(g(x))] = ?

Answer 14

f’(g(x)) * g’(x)

or

dy/dx = dy/du * du/dx

Question 15

d/dx[uⁿ] = ?

Answer 15

nu^n-1 * u’