Question

Calcule as derivadas das funções: a) f(x)=tg^2 (x^3+2); b) g(x)=(2x^3-5x^2+2x)^{\frac{3}{2}}; c) h(x)=ln(sen^4x+1); d) u(x) = (cosx+3)^5
OBS: É matéria de Cálculo 1!

Answer 1

a)
f(x) = tg²(x³ + 2)
f'(x) = ((tg²)'(x³ + 2)) . (tg'(x³ + 2)) . (x³ + 2)'
f'(x) = 2tg(x³ + 2). sec²(x³ + 2) . 3x²
f'(x) = 6x².sec²(x³+2).tg(x³+2)

b)
g(x) = (2x³ - 5x² + 2x)^(3/2)
g'(x) = (3/2).(2x³ - 5x² + 2x)^(1/2).(2x³ - 5x² + 2x)'
g'(x) = (3/2).(6x² - 10x + 2).(2x³ - 5x² + 2x)^(1/2)
g'(x) = $\frac{9x^2 - 15x + 3}{\sqrt{2x^3-5x^2+2x}}$

c)
h(x) = ln(sen^4(x+1))

h'(x) = $\frac{1}{sen^4(x+1)}.(sen^4(x+1))'$

h'(x) = $\frac{1}{sen^4(x+1)}.4.sen^3(x+1).cos(x+1).(x+1)'$

h'(x) = $4.\frac{1}{sen^4(x+1)}.sen^3(x+1).cos(x+1)$

h'(x) = $4.\frac{cos(x+1)}{sen(x+1)}$

d)
u(x) = (cos(x + 3)^5
u'(x) = 5.(cos (x + 3))^4 . (cos (x + 3))'
u'(x) = 5.(cos(x + 3))^4 . (-sen (x + 3)) . (x + 3)'
u'(x) = 5.(cos(x + 3))^4 . (-sen (x + 3)) . 1
u'(x) = -5.(cos(x + 3))^4.(sen (x + 3))