Question

1. Calcule a derivada das seguintes funcoes:
(a) f(x) = 6√x −7x5
(b) g(y) = (5 − 2y3)4
(c) h(x) =sec(x)(x3 − 7).
(d) F(x) =√3x − 2 · (4x − 3).

Answer 1

Para calcular as derivadas dessas funções, devemos aplicar a regra do produto e regra da cadeia:

a) f(x) = 6√x - 7x⁵

f(x) = 6.x^(1/2) - 7x⁵

f'(x) = 6.(1/2).x^(-1/2) - 5.7x⁴

f'(x) = 3/√x - 35x⁴

b) g(y) = (5 - 2y³)⁴

g'(y) = -6y.4.(5 - 2y³)³

g'(y) = -24y.(5 - 2y³)³

c) h(x) = sec(x).(x³ - 7)

h'(x) = tg(x).sec(x).(x³- 7) + sec(x).x²

h'(x) = sec(x)[tg(x)(x³ - 7) + x²]

d) f(x) = √(3x - 2).(4x - 3)

f(x) = (3x - 2)^(1/2).(4x - 3)

f'(x) = (1/2)(3x - 2)^(-1/2)(4x - 3) + √(3x - 2).4

f'(x) = (4x - 3)/(2√(3x-2)) + 4√(3x - 2)