Plot gradient vector in ContourPlot

[Lambda96]

TL;DR

Plot gradient vector in ContourPlot

Hi,

I have made the following ContourPlot in mathematica and now I wanted to $\vec{r}_1= \left(\begin{array}{c} -1 \\ 1 \end{array}\right)$, $\vec{r}_2= \left(\begin{array}{c} 0 \\ \sqrt{2} \end{array}\right)$ and $\vec{r}_3= \left(\begin{array}{c} 1 \\ 1 \end{array}\right)$ insert the gradient into the ContourPlot.

Is this possible and if so, how?

 

[Orodruin]

https://reference.wolfram.com/language/ref/ListVectorPlot.html

 

[Lambda96]

Thank you Orodruin for your help

Since I want to have the vectors at certain points in the ContourPlot, I used ListVectorPlot[{{x1,y1},{vx1,vy1}},...}].

Unfortunately, Mathematica then plots a vector field

 

[Orodruin]

Check out the VectorPoints option