Show that d²y/dx² / (dy/dx)⁴ is constant for x = t³+1, y = t²+1

[squenshl]

Homework Statement

A curve is defined by the parametric equations $x=t^3+1$ and $y=t^2+1$.
Show that $\frac{\frac{d^2y}{dx^2}}{\left(\frac{dy}{dx}\right)^4}$ is a constant.

Homework Equations

The Attempt at a Solution

So you differentiate both equations wrt $t$ then apply the chain rule to get $\frac{2}{3t}$. Applying the chain rule after differenating twice to get $\frac{d^2y}{dx^2}=\frac{1}{3t}$.
Substitute in both to get the result?

 

[Mark44]

Homework Statement

A curve is defined by the parametric equations $x=t^3+1$ and $y=t^2+1$.
Show that $\frac{\frac{d^2y}{dx^2}}{\left(\frac{dy}{dx}\right)^4}$ is a constant.

Homework Equations

The Attempt at a Solution

So you differentiate both equations wrt $t$ then apply the chain rule to get $\frac{2}{3t}$. Applying the chain rule after differenating twice to get $\frac{d^2y}{dx^2}=\frac{1}{3t}$.
Substitute in both to get the result?

Yes. Keep in mind that $\frac{d^2 y}{dx^2} = \frac d {dx} \left(\frac {dy}{dx}\right) \cdot \frac {dt}{dx}$, using the chain rule.

 

[squenshl]

Yes. Keep in mind that $\frac{d^2 y}{dx^2} = \frac d {dx} \left(\frac {dy}{dx}\right) \cdot \frac {dt}{dx}$, using the chain rule.

Got it thanks a lot