4

enter image description here

How can I plot this with \begin{tikzpicture}? the red line should be the derivative at x_0

Pls help :) Thanks!

Bernard
  • 271,350
Laura
  • 147
  • You mean TikZ. I believe the best way to plot anything in TikZ is to use PGFPlots. Read the relevant parts of the TikZ and PGFPlots manual and then either create a MWE(Minimal Working Example) and ask specific questions about your problems. Anyway this is a duplicate of several other questions - use the search box or google and you will find almost exactly what you need. – hpekristiansen Jun 23 '18 at 16:28
  • 3
    Tangent, or derivative? – Torbjørn T. Jun 23 '18 at 16:39
  • Please have a look here and here. –  Jun 23 '18 at 16:40
  • Other potentially interesting questions: https://tex.stackexchange.com/questions/401225 https://tex.stackexchange.com/questions/394368 https://tex.stackexchange.com/questions/99085 – Torbjørn T. Jun 23 '18 at 16:44
  • ah yea Tangent of course. I meant the gradient of cet tangent should be the derivative in x_0 and I had something in mind like making a variable m which always gives me the gradient at any x, it that possible? – Laura Jun 23 '18 at 16:51
  • The oldest similar question I found is this one from 2011. Probably we should mark this question as duplicate, but I don't want to do it alone. – Kpym Jun 23 '18 at 19:41
  • @Kpym I think that it is almost a duplicate, yet what was not in @Jake's fantastic answer is how to draw the tangent at a given x value. But yes, I should have remembered this post since I was already using it in another answer, so thanks for the reminder. ;-) –  Jun 23 '18 at 20:11

1 Answers1

6

TikZ automatically computes the tangent, for instance when using decorations, you are automatically in the "tangent space". So all you need to do is to add a marking consisting of a horizontal line in "tangent space".

\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}

enter image description here

Ah, and I should probably have mentioned that you can of course use this to draw the tangent at a fixed x value. Say you want to draw it at 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}

enter image description here

(Yes, it is possible to avoid drawing the plot twice. But all the possibilities will make the thing unnecessarily complex. And one could also avoid the hard coded length of the red line and avoid the \clip, but again the price to pay is an increase of complexity.)

And the nowadays mandatory animation can't be missing. ;-)

\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}

enter image description here