Title: CR_Diff_08
Course: Demonstrating STACK (v4.3.7)

Parametric differentiation

Find \(\frac{dy}{dx}\) in terms of [value] when \(x\) and \(y\) are related by the following pair of parametric equations: \[ x=[value]\] \[ y=[value]. \]
Feedback: If \(x\) and \(y\) are both functions of a parameter \(t\), then \[\frac{dy}{dx} = \frac{dy}{dt}/\frac{dx}{dt}\] \(y=[value]\) and \(x=[value]\), so \[\begin{array}{rcl}\displaystyle \frac{dy}{dx} &\displaystyle =&\displaystyle \frac{dy}{d[value]}/\frac{dx}{d[value]} \\ &\displaystyle =&\displaystyle \frac{d}{d[value]}[[value]]/\frac{d}{d[value]}[[value]] \\ &\displaystyle =&\displaystyle \frac[value][value] \\ &\displaystyle =&\displaystyle [value] \end{array}\]

Find \(\frac{dx}{dy}\) in terms of [value] when \(x\) and \(y\) are related by the following pair of parametric equations: \[ x=[value]\] \[ y=[value]. \]
Feedback: If \(x\) and \(y\) are both functions of a parameter \(t\), then \[\frac{dx}{dy} = \frac{dx}{dt}/\frac{dy}{dt}\] \(y=[value]\) and \(x=[value]\), so \[\begin{array}{rcl}\displaystyle \frac{dx}{dy} &\displaystyle =&\displaystyle \frac{dx}{d[value]}/\frac{dy}{d[value]} \\ &\displaystyle =&\displaystyle \frac{d}{d[value]}[[value]]/\frac{d}{d[value]}[[value]] \\ &\displaystyle =&\displaystyle \frac[value][value] \\ &\displaystyle =&\displaystyle [value] \end{array}\]