Question

Calcular derivada de f(x) = x² - 3x + 2 / 2x² + 5x - 1.

Answer 1

A derivada de um quociente é:
a/b = ba'-ab'/b²
Assim teremos:
[(2x²+5x-1)*(x²-3x+2)']-[(x²-3x+2)*(2x²+5x-1)']/(2x²+5x-1)²
[(2x²+5x-1)*(2x-3)]-[(x²-3x+2)*(4x+5)]/(2x²+5x-1)²
[4x³-6x²+10x²-15x-2x+3]-[4x³+5x²-12x²-15x+8x+10]/(2x²+5x-1)²
[4x³-4x³-6x²+10x²-5x²+12x²-15x-2x+15x-8x+3-10]/(2x²+5x-1)²
11x²-10x-7/(2x²+5x-1)²