Question

Find the second order derivative of y=2e^2x-3 log⁡(2x-3).

(a) 8e^2x+\(\frac{1}{(2x-3)^2}\)

(b) 8e^2x–\(\frac{12}{(2x-3)^2}\)

(c) e^2x+\(\frac{12}{(2x-3)^2}\)

(d) 8e^2x+\(\frac{12}{(2x-3)^2}\)

The question was posed to me in examination.

This question is from Second Order Derivatives topic in division Continuity and Differentiability of Mathematics – Class 12

Answer 1

The correct option is (d) 8e^2x+\(\frac{12}{(2x-3)^2}\)

To elaborate: Given that, y=2e^2x-3 log⁡(2x-3)

\(\frac{dy}{dx}\)=4e^2x-3.\(\frac{1}{(2x-3)}\).2=4e^2x–\(\frac{6}{(2x-3)}\)

\(\frac{d^2 y}{dx^2}=\frac{d}{dx} (\frac{dy}{dx})\)=8e^2x+\(\frac{12}{(2x-3)^2}\)