Question

Calcule a seguinte derivada:
I(x)=5x^3-6x+1 / 6x^3+2

Answer 1

Resposta:

y(x)=(5x^3-6x+1) / (6x^3+2)

Vou usar a regra do quociente

y'=[(5x^3-6x+1)'*(6x^3+2) - (5x^3-6x+1)*(6x^3+2)']/(6x^3+2)²

y'=[(15x²-6)*(6x^3+2) - (5x^3-6x+1)*(18x²)]/(6x^3+2)²

y'=[(90x^5+30x²-36x³-12) - (90x^5-108x³+18x²)]/(36x^6+24x³+4)

y'=[30x²-36x³-12 +108x³-18x²]/(36x^6+24x³+4)

y'=[72x³+12x²-12]/(36x^6+24x³+4)

y'=[18x³+3x²-3]/(9x^6+6x³+1)

y'=3*[6x³+x²-1]/(3x³+1)²