how to plot multiplication of two functions in latex

Question

I'm new to latex and am trying to plot

    f(x)=sqrt{2/pi}*exp{-x^2/2}

I managed to plot the exponential part easily but when I multiply it by the square root 4 errors occur. This is my code:

    \documentclass{standalone}
    \usepackage{pgfplots}
    \begin{document}
    \begin{tikzpicture}
    \begin{axis} [ 
    xmin=0,xmax=4, 
    xmin=0,xmax=0.9, 
    xlabel=$x$,
    ylabel={$ f(x)=exp(-x^2/2)*sqrt(2/\pi) $}
    ] 
    \addplot { exp(-x^2/2)*sqrt(2/\pi) };
    \end{axis}
    \end{tikzpicture}
    \end{document}

all errors occur in line 11:

Missing $ inserted \addplot {exp(-x^2/2)*sqrt(2/\pi)};
Math formula deleted: Insufficient symbol fonts \addplot {exp(-x^2/2)*sqrt(2/\pi)};
Illegal unit of measure (pt inserted) \addplot {exp(-x^2/2)*sqrt(2/\pi)};
Extra \else \addplot {exp(-x^2/2)*sqrt(2/\pi)};

and a warning:

running in backwards compatibility mode (unsuitable tick labels; missing features). Consider writing \pgfplotsset{compat=1.14} into your preamble.

I tried defining two functions and \addplot ing their multiplication but it didn't work, can anyone help me

Answer 1

Your error is pretty simple: You used a command to typeset the pi symbol instead of a value which can be multiplied. This code works:

\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis} [ 
xmin=0,xmax=4, 
xmin=0,xmax=0.9, 
xlabel=$x$,
ylabel={$ f(x)=exp(-x^2/2)*sqrt(2/\pi) $}
] 
\addplot { exp(-x^2/2)*sqrt(2/pi) };
\end{axis}
\end{tikzpicture}
\end{document}

Answer 2

This isn't really an answer, but since I notice quite a few mistakes, it might help you. Of course, the credit for solving your problem definitely goes to TeXnician. Let's begin.

What we will fix:

1. The redundant xmin, xmax
2. The faulty compilation of ylabel
3. The smoothness of your graph (OPTIONAL: I don't know if you want non-smooth graph for some personal reason)

For further explanation refer to my comment under your original question.

Here is the corrected code:

\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis} [ 
xmin=0,xmax=4, 
ymin=0,ymax=0.9, 
xlabel=$x$,
ylabel={$ f(x)=e^{-x^2/2} \cdot \sqrt{2/\pi} $},
axis lines=center,
axis equal
] 
\addplot[smooth, color=blue] { (exp(-x^2/2))*(sqrt(2/pi)) };
\end{axis}
\end{tikzpicture}
\end{document}

Explanations:

1. Replaced xmin=0,xmax=0.9 with ymin=0,ymax=0.9
2. Replaced ylabel={$ f(x)=exp(-x^2/2)*sqrt(2/\pi) $} with ylabel={$ f(x)=e^{-x^2/2} \cdot \sqrt{2/\pi} $}
3. Added smooth to the \addplot tag (note that the same result can be achieved with samples=<some number>, and it gives you more freedom of optimization; for example, samples=200 would yield a similar result)

NOTE: I also changed the color of the plot (by adding color=blue to \addplot tag) to clarify the situation as much as possible. I also added axis lines=center and axis equal for convenience reasons. The first one changes the form of the axes (central rather than on boundaries) and the second one sets axes ratio to 1:1. I just added these two tweaks to make the whole structure clearer.

EDIT: For the sake of newcomers, I added the result of the compilation: