Let $x(t) = 2t^2 + 2$, $y(t) = 3t^4 + 4t^3$. Find $\frac{d^2y}{dx^2}.$
My question is:
- Is this parameter function?
- I have tried to find the relationship between $x$ and $y$, but it seems this does not work. Is there any trick for such problem?
Let $x(t) = 2t^2 + 2$, $y(t) = 3t^4 + 4t^3$. Find $\frac{d^2y}{dx^2}.$
My question is:
$\dfrac{dy}{dx} = \dfrac{dy}{dt} \dfrac{dt}{dx}$ $\dfrac{d^2 y}{dx^2} = \dfrac{d\left(\dfrac{dy}{dt} \dfrac{dt}{dx} \right)}{dt} \dfrac{dt}{dx}$ Or in your case, you could relate $y$ and $x$ directly as $y = 3 \left(\dfrac{x-2}2 \right)^2 + 4\left(\dfrac{x-2}2 \right)^{3/2}$