If x = at^2 and y = 2at,then find frac{d^2 x} | vedclass

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(D) Given $x = at^2$ and $y = 2at$. First,find $\frac{dx}{dy}$ using the chain rule: $\frac{dx}{dy} = \frac{dx/dt}{dy/dt}$. Since $\frac{dx}{dt} = 2at

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$\frac{1}{2a}$

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(D) Given $x = at^2$ and $y = 2at$. First,find $\frac{dx}{dy}$ using the chain rule: $\frac{dx}{dy} = \frac{dx/dt}{dy/dt}$. Since $\frac{dx}{dt} = 2at$ and $\frac{dy}{dt} = 2a$,$\frac{dx}{dy} = \frac{2at}{2a} = t$. Now,differentiate $\frac{dx}{dy}$ with respect to $y$: $\frac{d^2 x}{dy^2} = \frac{d}{dy}(t) = \frac{d}{dt}(t) 	imes \frac{dt}{dy}$. Since $\frac{dt}{dy} = \frac{1}{dy/dt} = \frac{1}{2a}$,$\frac{d^2 x}{dy^2} = 1 	imes \frac{1}{2a} = \frac{1}{2a}$. Thus,the correct option is $D$.

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

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