Question

Determine a derivada no ponto especifico x=2
$f(x)= \frac{5x^{2} +3x-9 }{x^{2}+5 }$

Answer 1

f(x) = 5.x² +3.x -9 / x² +5

g(x) = 5.x² +3.x -9 -> g'(x) = 10.x +3

h(x) = x² +5 -> h'(x) = 2.x

g'(2) = 10.2 +3 -> g'(2) = 23

h'(2) = 2.2 -> h'(2) = 4

h(2) = 2² +5 -> h(2) = 9

g(2) = 5.2² +3.2 -9 -> g(2) = 17

-x-

f(x) = g(x) / h(x)

f'(x) = g'(x).h(x) -h'(x).g(x) / [ h(x)]²

f'(2) = 23.9 -4.17 / 9²

f'(2) = 207 -68 / 81

f'(2) = 139 / 81

Dúvidas só perguntar!