Question

If y=6x^2+3, then \(\left (\frac{dy}{dx}\right )^2=\frac{d^2 y}{dx^2}\).

(a) True

(b) False

I have been asked this question in exam.

The query is from Second Order Derivatives topic in portion Continuity and Differentiability of Mathematics – Class 12

Answer 1

Right choice is (b) False

The best explanation: The given statement is false. Given that, y=6x^2+3

\(\frac{dy}{dx}\)=12x

⇒\(\left (\frac{dy}{dx}\right )^2=(12x)^2=144x^2\)

\(\frac{d^2 y}{dx^2}=\frac{d}{dx}\) (12x)=12

∴\(\left (\frac{dy}{dx}\right )^2≠\frac{d^2 y}{dx^2}\)