Give the specific higher - order derivative of the given functions:

Question

a. 𝑓(𝑥) = 6𝑥^5 + 3𝑥^4 − 2𝑥^3 + 5𝑥^2 − 8𝑥 + 9 ; 𝒇^(𝟒) (𝒙)

b. 𝑓(𝑥) = 2𝑥^7 − 𝑥^5 + 5𝑥^3 − 8𝑥 + 4; 𝒇^(5) (𝒙)

c. ℎ(𝑥) = (𝑥^5 − 1/15𝑥^5 ) ;𝒉^(𝟒) (𝒙)

Answer 1

f(x) = 6x^5 + 3x^4 -2x^3 +5x^2 - 8x + 9

f^iv(x) is the 4th derivative. That's probably what you meant by f^4(x)

f'(x) = 30x^4 +12x^3 - 6x^2 +10x -8

f"(x) = 120x^3 +36x^2 -12x + 10

f^"'(x) = 360x^2 + 72x -12

f^iv(x) = 720x +72 = the 4th derivative

f(x) = 2x^7 -x^5 +5x^3 - 8x + 4

f'(x) = 14x^6 -5x^4 +15x -8

f"(x) = 84x^5 -20x^3 +15

f"'(x) = 420x^4 -60x^2

f'^v(x) = 1680x^3 - 120x = the 4th derivative

f^v(x) = 5040x^2 -120 = 5th derivative

h(x) = (x^5 - 1)/15x^5 = 1/15 - (1/15)x^-5

h'(x) = (1/3)x^-6

h"(x) = -2x^-7

h"'(x) =14x^-8

h'^v(x) = -112x^-9 = -112/x^9

UNLESS you really meant

h(x) = x^5 -1/15x^5 = x^5 -(1/15)x^-5

h'(x) = 5x^5 +(1/3)x^-6

h"(x) = 25x^5 -2x^-7

h"'(x) = 125x^4 +14x^-8

h'^v(x) = 500x^3 - 112x^-9 = 500x^3 -112/x^9 = 4th derivative