Derivatives

Question 1

If f(x) = c then f’(x) = __

Answer 1

f’(x) = 0

Question 2

If f(x) = xⁿ then f’(x) = __

Answer 2

f’(x) = nxⁿ⁻¹

Question 3

If f(x) = c ⋅xⁿ then f’(x) = __

Answer 3

f’(x) = c ⋅nxⁿ⁻¹

Question 4

If f(x) = u(x) ± v(x) then f’(x) =

Answer 4

f’(x) = u’(x) ± v’(x)

Question 5

If f(x) = u(x) ⋅ v(x) then f’(x) = __

Answer 5

f’(x) = u(x) ⋅ v’(x) + v(x) ⋅ u’(x)

Question 6

If f(x) = u(x) / v(x) then f’(x) = __

Answer 6

f’(x) = (v(x) ⋅ u’(x) - u(x) ⋅ v’(x)) / (v(x))²

Question 7

If f(x) = sin x then f’(x) = __

Answer 7

f’(x) = cos x

Question 8

If f(x) = cos x then f’(x) = __

Answer 8

f’(x) = -sin x

Question 9

If f(x) = tan x then f’(x) = __

Answer 9

f’(x) = sec² x

Question 10

If f(x) = cot x then f’(x) = __

Answer 10

f’(x) = -csc² x

Question 11

If f(x) = sec x then f’(x) = __

Answer 11

f’(x) = sec x ⋅ tan x

Question 12

If f(x) = csc x then f’(x) = __

Answer 12

f’(x) = -csc x ⋅ cot x

Question 13

If f(n) = aⁿ then f’(n) = __

Answer 13

f’(n) = aⁿ ⋅ ln a

Question 14

If f(n) = eⁿ then f’(n) = __

Answer 14

f’(n) = eⁿ

Question 15

If f(x) = ln x then f’(x) = __

Answer 15

f’(x) = 1 / x

Question 16

If f(x) = log(base b)x then f’(x) = __

Answer 16

f’(x) = 1 / (x ⋅ ln b)

Question 17

If h(x) = f(g(x)) then h’(x) = __

Answer 17

h’(x) = f’(g(x))⋅g’(x)

Question 18

If f(x) = arcsin x then f’(x) = __

Answer 18

f’(x) = 1 / √(1-x²) (think more generally)

Question 19

If f(x) = arccos x then f’(x) = __

Answer 19

f’(x) = -1 / √(1-x²) (think more generally)

Question 20

If f(x) = arctan x then f’(x) = __

Answer 20

f’(x) = 1 / (1 + x²) (think more generally)

Question 21

If f(x) = arccot x then f’(x) = __

Answer 21

f’(x) = -1 / (1 + x²) (think more generally)

Question 22

If f(x) = arcsec x then f’(x) = __

Answer 22

f’(x) = 1 / (x√(x²-1)) (think more generally)

Question 23

If f(x) = arccsc x then f’(x) = __

Answer 23

f’(x) = -1 / (x√(x²-1)) (think more generally)