There is a topic on the subject here however, the proposed solutions either don't provide the same functionality as the code below or don't use ggplot.

There is a topic on the subject here however, the proposed solutions either don't provide the same functionality as the code below or don't use ggplot.

//The next step is important to understand:
//The goal is have arrows that have approx. the same length (c = const) and
//point to the direction of f_prime at some point (x,y) for all points
//Note: f_prime is the derivative of F(x,y) with respect to x,
//hence f_prime provides the relative change in y as a result of a change in x
//Now the problem to draw the arrows can be formulated using f_prime (= dy/dx) 
//and the fact that c^2 = dy^2 + dx^2 (Pythogoras)
//Using basic algebra to solve the problem:
//Solve for dx = dy/f_prime(x,y) and insert into
//c^2 = dy^2 + dx^2 = dy^2 + (dy/f_prime(x,y))^2 and solve for dx
//dx = sqrt(c^2/(1+f(x,y)^2) and
//dy = f(x,y)*dx
//now we can draw the arrows using (x,y) as the start and (x+dx, y+dy) as the end
//translating this into code:
data$dx <- sqrt((1/len)/(1+data$dydx^2))
data$dy <- data$dx*data$dydx
ggplot(data=data, aes(x=x,y=y), environment = environment()) + 
 geom_point(size = 1) + 
 geom_segment(aes(xend=x+dx, yend=y+dy), arrow = arrow(length = unit(0.1, "cm"))) + 
 xlim(minX,maxX) + 
 ylim(minY,maxY) 

Maybe there is a better/fast more elegant way to do it, if yes please share if not happy to help.

//The next step is important to understand:
//The goal is have arrows that have approx. the same length (c = const) and
//point to the direction of f_prime at some point (x,y) for all points
//Note: f_prime is the derivative of F(x,y) with respect to x,
//hence f_prime provides the relative change in y as a result of a change in x
//Now the problem to draw the arrows can be formulated using f_prime (= dy/dx) 
//and the fact that c^2 = dy^2 + dx^2 (Pythagoras)
//Using basic algebra to solve the problem:
//Solve for dx = dy/f_prime(x,y) and insert into
//c^2 = dy^2 + dx^2 = dy^2 + (dy/f_prime(x,y))^2 and solve for dx
//dx = sqrt(c^2/(1+f(x,y)^2) and
//dy = f(x,y)*dx
//now we can draw the arrows using (x,y) as the start and (x+dx, y+dy) as the end
//translating this into code:
data$dx <- sqrt((1/len)/(1+data$dydx^2))
data$dy <- data$dx*data$dydx
ggplot(data=data, aes(x=x,y=y), environment = environment()) + 
 geom_point(size = 1) + 
 geom_segment(aes(xend=x+dx, yend=y+dy), arrow = arrow(length = unit(0.1, "cm"))) + 
 xlim(minX,maxX) + 
 ylim(minY,maxY) 

Maybe there is a better/faster more elegant way to do it, if yes please share if not happy to help.