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Illustration Vector plot of the gradient of the scalar function x²+5xy

<span>Vector plot of the gradient of the scalar function x²+5xy</span>
Vector plot of the gradient of the scalar function x²+5xy
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This is how the gradient field \(\nabla f \) in the interval \(x,y \in [0,1]\) of the following two-dimensional scalar function \(f\) looks like:$$ f(x,y) = x^2 + 5x\,y $$

It can be clearly seen that as the distance from the location (0,0) increases, the length of the vector arrows (i.e. the size of the slope) increases.