Question Detail
Question
Differentiate y = log (x³-x) + 72/3∗x
Correct Answer
Option D is the correct answer.
Detailed Explanation
We differentiate each term separately. Assume 'log' refers to the natural logarithm (ln).For the first term, y1 = ln(x³-x):dy1/dx = (1/(x³-x)) * d/dx(x³-x) (using chain rule for ln(u))= (1/(x(x²-1))) * (3x²-1)= (3x²-1) / (x(x²-1))For the second term, y2 = 7(2/3)x:dy2/dx = 7(2/3)x * ln(7) * (2/3) (using d/dx(aku) = aku * ln(a) * k)Combining both derivatives:dy/dx = (3x²-1) / (x(x²-1)) + (2/3)ln(7) * 7(2/3)x.This matches option D, interpreting 'log7' as 'ln(7)'.
Hint
Remember the chain rule for logarithmic functions (d/dx ln(u) = u'/u) and the differentiation rule for exponential functions (d/dx au = au ln(a) u').