如何绘制函数及其导数

Question

我该如何绘制这个图\begin{tikzpicture}？红线应该是 x_0 处的导数

请帮忙:) 谢谢！

Answer 1

钛钾Z 会自动计算切线，例如，当使用装饰时，您会自动处于“切线空间”。因此，您需要做的就是在“切线空间”中添加由水平线组成的标记。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.markings}
\tikzset{tangent/.style={postaction={decorate,decoration={markings,
     mark=at position #1 with {
     \draw[red] (0pt,0pt) coordinate (Tang) -- (200pt,0pt);)}}}}}

\begin{document} 
\begin{tikzpicture}[declare function={f(\x)=3*sin(10*\x+20);}]
\draw[latex-latex] (0,5) -- (0,0) -- (8,0);
\begin{scope}
\clip (0,0) rectangle (7,5);
\draw[tangent=0.2] plot[samples=100,domain=0:7] ({\x},{f(\x)});
\end{scope}
\draw[dashed] (Tang) --(0,-0.1 -| Tang) node[below]{$x_0$};
\end{tikzpicture} 
\end{document} 

啊，我可能应该提到，你当然可以使用它在固定x值处绘制切线。假设你想在 处绘制它x=1.3。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.markings}
\tikzset{tangent/.style={postaction={decorate,decoration={markings,
     mark=at position #1 with {
     \draw[red] (0pt,0pt) coordinate (Tang) -- (200pt,0pt);)}}}}}

\begin{document} 
\begin{tikzpicture}[declare function={f(\x)=3*sin(10*\x+20);}]
\draw[latex-latex] (0,5) -- (0,0) -- (8,0);
\begin{scope}
\clip (0,0) rectangle (7,5);
\draw plot[samples=100,domain=0:7] ({\x},{f(\x)});
\path[tangent=0] plot[samples=100,domain=1.3:7] ({\x},{f(\x)});
\end{scope}
\draw[dashed] (Tang) --(0,-0.1 -| Tang) node[below]{$x_0=1.3$cm};
\end{tikzpicture} 
\end{document} 

（是的，可以避免绘制两次图。但所有可能性都会使事情变得不必要地复杂。并且可以避免红线的硬编码长度并避免\clip，但同样要付出的代价是复杂性的增加。）

而如今强制性的动画是不能缺少的。;-)

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.markings}
\tikzset{tangent/.style={postaction={decorate,decoration={markings,
     mark=at position #1 with {
     \draw[red] (0pt,0pt) coordinate (Tang) -- (200pt,0pt);)}}}}}

\begin{document}
\foreach \X in {0.5,0.6,...,6} 
{\begin{tikzpicture}[declare function={f(\x)=3*sin(10*\x+20);}]
\draw[latex-latex] (0,5) -- (0,0) -- (8,0);
\begin{scope}
\clip (0,0) rectangle (7,5);
\draw plot[samples=100,domain=0:7] ({\x},{f(\x)});
\path[tangent=0] plot[samples=100,domain={\X}:7] ({\x},{f(\x)});
\end{scope}
\pgfmathsetmacro{\Y}{int(10*\X)}
\draw[dashed] (Tang) --(0,-0.1 -| Tang) node[below]{$x_0=\Y$mm};
\end{tikzpicture}}
\end{document}