Question Detail
Question
Using first principle, evaluate Δx/Δy of the derivative of ln(3x+1)
Correct Answer
Option B is the correct answer.
Detailed Explanation
From y=ln(3x+1), x=(eʸ-1)/3. Then Δx/Δy = [x(y+Δy)-x(y)]/Δy = eʸ(e^Δy-1)/(3Δy). Expanding e^Δy-1 as a series and dividing by Δy gives (eʸ/3)[1+Δy/2!+(Δy)²/3!+(Δy)³/4!+...].
Hint
Solve the log equation for x in terms of y, then expand e^Δy as a Maclaurin series.