Question

8). Encontre a derivada das funções, a seguir:
a) f(x)=(3x+1)^2
b) f(x)=V([13x]^2-5x+8)
c) f(x)=2(x+1)
d) f(x)=x^2/(3x-1)

Answer 1

a)
f(x)=(3x+1)^2
f(x) ' = 2.(3x+1).3
f(x)' = 6.(3x+1)
f(x)'=18x+6

b)
$f(x) = \sqrt{(13x)^2-5x+8}\\ \\ f(x) = ((13x)^2-5x+8)^{ \frac{1}{2} } \\ \\ f(x)' = \frac{1}{2}. ((13x)^2-5x+8)^{ -\frac{1}{2} }. (2.169x-5)$

c)
f(x) = 2(x+1)
f(x)'=2

d)
$f(x) = \frac{ x^{2} }{3x-1}\\ \\ f(x)'= \frac{2x.(3x-1)- 3.x^{2} }{ (3x-1)^{2} } \\ \\ f(x)'= \frac{6 x^{2} -2x-3 x^{2} }{(3x-1)^{2}}\\ \\ f(x)'= \frac{3 x^{2} -2x }{(3x-1)^{2}}$