Final answer:
The derivative of y = ln(2x² - x) + 3x is dy/dx = (4x - 1) / (2x² - x) + 3, applying the chain rule for the logarithmic part and the power rule for the polynomial part.
Step-by-step explanation:
The problem asks us to find the derivative of the function y = ln(2x² - x) + 3x. This calculation will involve using the rules of derivatives for logarithmic functions and polynomials. To find the derivative, we apply the chain rule for the logarithmic part and the power rule for the polynomial part.
Using the chain rule, the derivative of ln(2x² - x) is 1/(2x² - x) multiplied by the derivative of the inside function (2x² - x), which is 4x - 1. Therefore, this part of the derivative simplifies to (4x - 1) / (2x² - x). For the polynomial part, the derivative of 3x is simply 3.
Adding these two parts together gives us the final derivative: dy/dx = (4x - 1) / (2x² - x) + 3.