Question

Find the second order derivative of y=9 log⁡ t^3.

(a) \(\frac{27}{t^2}\)

(b) –\(\frac{27}{t^2}\)

(c) –\(\frac{1}{t^2}\)

(d) –\(\frac{27}{2t^2}\)

This question was posed to me in an interview for internship.

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

Answer 1

Correct choice is (b) –\(\frac{27}{t^2}\)

To explain: Given that, y=9 log⁡t^3

\(\frac{dy}{dx}=9.\frac{1}{t^3}.3t^2=\frac{27}{t}\)

\(\frac{d^2 y}{dx^2}=27(-\frac{1}{t^2})=-\frac{27}{t^2}\).