Question Detail
Question
Find d/dx(ln(x³) + ln(7x))
Correct Answer
Option B is the correct answer.
Detailed Explanation
First, simplify the expression using logarithm properties:ln(ab) = b ln(a)ln(ab) = ln(a) + ln(b)So, ln(x³) + ln(7x) = 3 ln(x) + (ln(7) + ln(x))= 3 ln(x) + ln(7) + ln(x)Combine the ln(x) terms:= 4 ln(x) + ln(7)Now, differentiate this simplified expression with respect to x:d/dx(4 ln(x) + ln(7)) = 4 * d/dx(ln(x)) + d/dx(ln(7))= 4 * 1/x + 0 (since ln(7) is a constant)= 4/x. This matches option B.
Hint
Use logarithm properties (ln(ab) = b ln(a) and ln(ab) = ln(a) + ln(b)) to simplify the expression before differentiating. Remember that the derivative of ln(x) is 1/x, and the derivative of a constant is 0.