Question Detail

We differentiate each term separately. Assume 'log' refers to the natural logarithm (ln) as is common in calculus context unless a base is specified in the derivative formulas.For the first term, y1 = ln(x3 - x):dy1/dx = (1 / (x3 - x)) * (d/dx [x3 - x]) = (3x2 - 1) / (x(x2 - 1)).For the second term, y2 = 7(2x/3):dy2/dx = 7(2x/3) * ln(7) * (d/dx [2x/3]) = 7(2x/3) * ln(7) * (2/3).The question options replace ln(7) with 'log7'. Assuming log7 here means ln(7), we combine the derivatives:dy/dx = (3x2 - 1) / (x(x2 - 1)) + 7(2x/3) * (2/3)log7.