Question

Utilizando a regra do quociente, calcule a derivada da função ANEXO. Assinale a resposta:
(A) e^2x (2x + 1) / 3x²

(B) e^2x (2x - 1) / 9x²

(C) e^2x (2x - 1) / 3x²

(D) e^2x (2x + 1) / 9x²

(E) 2e^2x (2x - 1) / 3x²

Answer 1

Y = e^(2×)/3x => Y' = [ e^(2×)'(2x)'*(3x) - e^(2×)*(3x)' ]/(3x)^2 => Y' [ e^(2×)*2(3x) - e^(2×)*3 ]/9x^2 => Y' [ 6xe^(2×) - 3e^(2×) ]/9x^2 => 3e^(2×)[ 2x -1]/9x^2 => e^(2×)[ 2x - 1]/3x^2. Letra C)

Answer 2

y = (e^2x)/3x

y ' = [(2e^2x).3x - 3.e^2x]/(3x)²

y ' = [6xe^2x) - 3.e^2x]/9x²

y ' = 3[2xe^2x) - e^2x]/9x²

y ' = [2xe^2x) - e^2x]/3x²

y ' = e^2x[2x) - 1]/3x²