Question Detail
Question
Find the derivative of y = 3 log(x - 1).
Correct Answer
Option C is the correct answer.
Detailed Explanation
Assuming 'log' refers to the natural logarithm (ln), which is common in calculus:y = 3 ln(x - 1).Using the chain rule, the derivative is:dy/dx = d/dx [3 ln(x - 1)] = 3 * (1/(x - 1)) * d/dx(x - 1) = 3 * (1/(x - 1)) * 1 = 3/(x - 1).If 'log' referred to log10, the derivative would be 3/((x-1)ln10), which is not an option. Thus, 'log' is implied to be 'ln'.
Hint
Recall the derivative of ln(u) is (1/u) * du/dx. Assume 'log' means natural logarithm.