If x = t2, y = t3, then \(\frac{d^2y}{dx^2}=\)A. \(\frac{3}{4}\)B.

1.	If x = t2, y = t3, then \(\frac{d^2y}{dx^2}=\)A. \(\frac{3}{4}\)B. \(\frac{3}{4t}\)C. \(\frac{3}{2t}\)D.\(\frac{3t}{2}\)
Answer» Correct Answer is (A) \(\frac{3}{4}\) \(x=t^2;y=t^3\) \(\frac{dy}{dt}=3t^2;\frac{dx}{dt}=2t\) \(\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\)\(=\frac{3t}{2}\) \(\frac{d^2y}{dx^2}=\frac{\frac{d}{dt}(\frac{dy}{dx})}{\frac{dx}{dt}}\)\(=\frac{\frac{3t}{2}}{2t}\) \(=\frac{3}{4}\)

If x = t2, y = t3, then \(\frac{d^2y}{dx^2}=\)A. \(\frac{3}{4}\)B. \(\frac{3}{4t}\)C. \(\frac{3}{2t}\)D.\(\frac{3t}{2}\)

Answer»

Correct Answer is (A) \(\frac{3}{4}\)

\(x=t^2;y=t^3\)

\(\frac{dy}{dt}=3t^2;\frac{dx}{dt}=2t\)

\(\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\)\(=\frac{3t}{2}\)

\(\frac{d^2y}{dx^2}=\frac{\frac{d}{dt}(\frac{dy}{dx})}{\frac{dx}{dt}}\)\(=\frac{\frac{3t}{2}}{2t}\)

\(=\frac{3}{4}\)