Question

x=at^2 y=2at then d^2y/dx^2

Answer 1

here is ur answer........

Answer 2

Answer:

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

Step-by-step explanation:

We have been given that

$x=at^2,y=2at$

On differentiating, we get

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

Hence, we have

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

Now, using the formula

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

Plugging the values, we get

$\frac{d^2y}{dx^2}=\frac{d}{dt}(1/t)\cdot\frac{1}{2at}\\\\\frac{d^2y}{dx^2}=-\frac{1}{t^2}\cdot\frac{1}{2at}\\\\\frac{d^2y}{dx^2}=-\frac{1}{2at^3}$