Finding $\frac{d^2 y}{dx^2}$ I am not sure how to do this but I need to find $\frac{dy}{dx}$ and $\frac{d^2 y}{dx^2}$
For $x = t^2 + 1, y= t^2+t$
And then show what t values gives a concave upward.
I know the simple formula to find $\frac{dy}{dx}$
I get $$\frac{dy}{dx} = \frac{y'}{x'}$$
$$\frac{dy}{dx} = \frac{2t+1}{2t}$$
$$\frac{d^2 y}{dx^2} = \frac{\frac{dy}{dx}}{dx}$$
$$\frac{\frac{2t+1}{2t}}{2t}$$
This is wrong and I am not sure why, they end with a negative number which makes no sense to me.

Note that $$\frac{d^2y}{dx^2}=\frac{d}{dx}(\frac{dy}{dx})=\frac{d}{dt}(\frac{dy}{dx}).\frac{dt}{dx}=\frac{d}{dt}(\frac{2t+1}{2t}).\frac{1}{2t}=....$$
