My professor gave us a sheet that had the calculus of functions in different formats. The sheet isn't making any sense to me though.

$\displaystyle x=f(t)$

$\displaystyle y=g(t)$

Derivatives: $\displaystyle \frac{dy}{dt}=f'(t)$, $\displaystyle \frac{dx}{dt}=g'(t)$, $\displaystyle \frac{dy}{dx}=\frac{f'(t)}{g'(t)}$

Integrals: $\displaystyle \int_ \alpha ^ \beta g(t)f'(t)dt$

Arc Length: $\displaystyle \int_ \alpha ^ \beta \sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy} {dt}\right)^2} dt$

Should the letters correspond?

x goes with f

y goes with g