Question

If y=log⁡(2x^3), find \(\frac{d^2 y}{dx^2}\).

(a) –\(\frac{2}{x^2}\)

(b) \(\frac{3}{x^2}\)

(c) \(\frac{2}{x^2}\)

(d) –\(\frac{3}{x^2}\)

I have been asked this question during an interview.

My doubt is from Second Order Derivatives topic in chapter Continuity and Differentiability of Mathematics – Class 12

Answer 1

Right answer is (d) –\(\frac{3}{x^2}\)

For explanation I would say: Given that, y=log⁡(2x^3)

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

\(\frac{d^2 y}{dx^2}=-\frac{3}{x^2}\)