매개변수 함수 미분

$\displaystyle x = 3 t - \frac{1}{t}$, $y = te ^{t - 1}$ $\displaystyle \frac{dx}{dt} = 3 + \frac{1}{t ^{2}}$, $\displaystyle \frac{dy}{dt} = e ^{t - 1} + te ^{t - 1}$ $\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{e ^{t - 1} + te ^{t - 1}}{3 + \frac{1}{t ^{2}}} = \frac{\left( t ^{2} + t ^{3} \right) e ^{t - 1}}{3 t ^{2} + 1}$ 따라서 $t = 1$일 때, $\displaystyle \frac{dy}{dx} = \frac{1}{2}$