Derivative of ln(3x^2 + 2x) - Step-by-Step Solution

To find dy/dx for the equation y = ln(3x^2 + 2x), we can use the chain rule.\n\nLet u = 3x^2 + 2x.\nTo find du/dx, we can differentiate u with respect to x:\ndu/dx = d(3x^2 + 2x)/dx = 6x + 2.\n\nNow, let y = ln(u).\nTo find dy/du, we differentiate y with respect to u:\ndy/du = 1/u.\n\nFinally, using the chain rule, we can find dy/dx:\ndy/dx = (dy/du) * (du/dx)\n = (1/u) * (6x + 2)\n = (6x + 2)/(3x^2 + 2x).\n\nTherefore, dy/dx for the equation y = ln(3x^2 + 2x) is (6x + 2)/(3x^2 + 2x).