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Differentiate each term separately. Assume "log" refers to the natural logarithm (ln), as is common in calculus when no base is specified. If it were base 10, it would be log10. The derivative of logb(u) is (1/(u ln b)) du/dx. For ln(u), it is (1/u) du/dx. For d/dx(au) = au ln(a) du/dx.1. d/dx [log(x3 - x)]: Using the chain rule, this is (1/(x3 - x)) * d/dx(x3 - x) = (1/(x(x2 - 1))) * (3x2 - 1) = (3x2 - 1) / (x(x2 - 1))2. d/dx [7(2/3)x]: Using the formula d/dx(au) = au ln(a) du/dx. Here a=7, u=(2/3)x, so du/dx = 2/3. = 7(2/3)x * ln(7) * (2/3)Combine the derivatives:dy/dx = (3x2 - 1) / (x(x2 - 1)) + 7(2/3)x (2/3) ln(7).Since ln(7) can be written as log 7 (if 'log' refers to natural logarithm in the context of the options), this matches option D.