一般地，

<script type="math/tex; mode=display" id="MathJax-Element-764">f(n) = \begin{cases} x = \varphi(t) \\ y = \phi(t) \end{cases}</script>
确定y<script type="math/tex" id="MathJax-Element-765">y</script>与x<script type="math/tex" id="MathJax-Element-766">x</script>间的函数关系，则称此函数关系所表达的函数为由参数方程所确定的函数.

假定φ(t)和ϕ(t)<script type="math/tex" id="MathJax-Element-767">\varphi(t) 和 \phi(t)</script>都可导，且φ′(t)≠0<script type="math/tex" id="MathJax-Element-768">\varphi'(t) \neq 0</script>，则有

<script type="math/tex; mode=display" id="MathJax-Element-769">\frac{dy}{dx} = \frac{dy}{dt}·\frac{dt}{dx} = \frac{dy}{dt}·\frac{1}{\frac{dx}{dt}} = \frac{\phi'(t)}{\varphi'(t)}</script>即 <script type="math/tex; mode=display" id="MathJax-Element-770">\frac{dy}{dx} = \frac{\phi'(t)}{\varphi'(t)}</script>上式也可以写成 <script type="math/tex; mode=display" id="MathJax-Element-771">\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}</script>
这就是由参数方程所确定的x<script type="math/tex" id="MathJax-Element-772"></script>的函数的导数公式.