∂ 导数计算器Derivative Calculator
求函数的导数：支持多项式、三角、指数、对数和复合函数，可求 1–5 阶导数并代入某点求导数值，结果自动化简并给出 LaTeX。Differentiate functions — polynomials, trig, exponential, logarithmic and composite — up to the 5th derivative, evaluate at a point, with simplified results and LaTeX.
使用说明与常见问题How-to & FAQ
「导数计算器」是什么？What is the Derivative Calculator tool?
求函数的导数：支持多项式、三角、指数、对数和复合函数，可求 1–5 阶导数并代入某点求导数值，结果自动化简并给出 LaTeX。Differentiate functions — polynomials, trig, exponential, logarithmic and composite — up to the 5th derivative, evaluate at a point, with simplified results and LaTeX.
如何使用「导数计算器」？How do I use the Derivative Calculator tool?
在「导数计算器」中，按需设置「函数 f(x)」、「变量」、「阶数」、「代入点（可选）」等选项，然后点击「求导」按钮即可。In the Derivative Calculator: Set "Function f(x)", "Variable", "Order", "At point (optional)", then click "Differentiate".
结果和课本写法不一样？Why does the result look different from my textbook?
同一个导数可以有多种等价写法，例如 2*sin(x)*cos(x) 与 sin(2x)；工具会自动化简，但不一定化成你期望的形式。可以把两种写法代入同一个点比较数值来确认。The same derivative has many equivalent forms (2*sin(x)*cos(x) vs sin(2x)). Results are simplified automatically but may not match your preferred form; compare both at the same point to confirm.
支持哪些写法？What syntax is supported?
四则运算 + - * /、乘方 ^、括号，函数 sin cos tan asin acos atan sinh cosh tanh sqrt abs exp log（自然对数，ln 也可以）等，常数 pi 和 e。乘号可以省略（2x、3sin(x)），也可以用 ×、÷、π、√。+ - * /, powers with ^, parentheses, functions such as sin cos tan asin acos atan sinh cosh tanh sqrt abs exp log (natural log; ln also works), and the constants pi and e. Multiplication can be implicit (2x, 3sin(x)); ×, ÷, π and √ are accepted too.
用的是什么计算引擎？What engine does it use?
开源符号计算库 nerdamer（Apache-2.0 许可），在独立的后台线程（Web Worker）中运行，超过 10 秒会自动停止，不会卡住页面；所有计算都在本地完成。The open-source symbolic library nerdamer (Apache-2.0), running in a background Web Worker that stops after 10 seconds so the page never freezes; everything is computed locally.
计算精度如何？How precise are the results?
「导数计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Derivative Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「导数计算器」免费吗？需要注册吗？Is the Derivative Calculator free? Do I need an account?
「导数计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Derivative Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.