If $x=at^2$ and $y=2at,$ then $\frac{d^2

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

If $x=at^2$ and $y=2at,$ then $\frac{d^2y}{dx^2}=$

Options:

$-\frac{1}{t^2}$

$-\frac{1}{2at^3}$

$-\frac{t^3}{2a}$

Correct Answer:

$-\frac{1}{2at^3}$

Explanation:

The correct answer is Option (3) → $-\frac{1}{2at^3}$

$x=at^2$ and $y=2at$

$\frac{dx}{dt}=2at$, $\frac{dy}{dt}=2a⇒\frac{dy}{dx}=\frac{1}{t}$

$\frac{d^2y}{dx^2}=-\frac{1}{t^2}×\frac{dt}{dx}$

$=-\frac{1}{2at^3}$