PROPRIEDADES DE DERIVADAS

PROPRIEDADES DE DERIVAÇÃO

Utilize as propriedades operatórias de derivação e determine a derivada das funções a seguir:

F (x) = 4x 11

f' (x) = 11.4x11-1

f' (x) = 44x10

F (x) = 2 + 3x2 + 2x3

f' (x) = 2.3x2-1 + 3.2x3-1

f' (x) = 6x + 6x2

F (x) = _ 3 x2 + √5

4 7

f' (x) = 2.(_ 3 )x2-1 + 51/2

4 7

f' (x) = _ 6x + 1 .5 -1/2

4 2 7

f' (x) = _ 3x +7 -1/2

2 7

f' (x) = _ 3x

2

F (x) = x2 + 1

x – 1

U = x2 + 1 → U’ = 2x f’ (x) = U’.V – U.V’

V = x – 1 → V’ = 1 V2

f' (x) = 2x. (x – 1) – (x2 + 1).1

(x – 1)2

f' (x) = 2x2 – 2x – x2 - 1

(x – 1)2

f' (x) = x2 – 2x - 1

(x – 1)2

F (x) = 2

x4

f' (x) = 2.x-4

f' (x) = -4.(2).x-4-1

f' (x) = -8x-5 →_ 8

x5

F (x) = x + 1

x – 1

U = x + 1 → U’ = 1 f’ (x) = U’.V – U.V’

V = x – 1 → V’ = 1 V2

f' (x) = 1. (x – 1) – (x + 1).1

(x – 1)2

f' (x) = x – 1 – x – 1

(x – 1)2

f' (x) = – 2

(x – 1)2

F (x) = (x2 – 1) . (x2 + x)

U = x2 - 1 → U’ = 2x f’ (x) = U’.V + U.V’

V = x2 + x → V’ = 2x + 1

f' (x) = 2x. (x2 + x) + (x2 - 1).(2x + 1)

f' (x) = 2x3 + 2x2 + 2x3 + x2 – 2x - 1

f' (x) = 4x3 + 3x2 – 2x - 1

F (x) = (2x2 – 1) . (x + 1)