Hi all,

I want to understand more of tangent line / gradient line then read the wikipedia and saw the animation here for the tangent line:

I create the plot (static image):

```
using Plots, LaTeXStrings
gr()
f(x) = -x^2 + 2x + 2
f'
# gradient_line(f, x₀) is a tangent line with an intercept at point x₀
# in other words it will pass x₀
# and a slope of f'(x₀) - essentially your usual y = a + bx
# where a is the value of the actual function at the point x₀ through
# which we want the line to pass,
# b is the derivative of the function at that point,
# and the "x" in y=a+bx is replaced by x-x₀
# because our "origin" is the point at which we're taking the tangent.
gradient_line(f, x₀) = (x -> f(x₀) + f'(x₀)*(x-x₀))
default(markerstrokecolor = "white", linewidth = 2);
#Plot f
plot(f, -3:0.1:5, label = "f(x) = -x² + 2x + 2", xlabel = "x", ylabel = "f(x)");
# Plot tangent lines
scatter!([-1], [f(-1)], label = "", markersize = 5);
plot!(gradient_line(f, -1), -3:0.1:0.5, label = "f'(-1)", color = 2);
scatter!([1/2], [f(1/2)], label = "", markersize = 5, color = 3);
plot!(gradient_line(f, 1/2), -1:0.1:2, label = "f'(1/2)", color = 3)
scatter!([2], [f(2)], label = "", markersize = 5, color = 4);
plot!(gradient_line(f, 2), 0.2:0.1:3, label = "f'(2)", color = 4)
scatter!([3], [f(3)], label = "", markersize = 5, color = 5);
plot!(gradient_line(f, 3), 0.8:0.1:4, label = "f'(3)", color = 5)
```

Now, I want to create the moving tangent lines animation, but there is an error, which I have no idea why it said missing comma or ), it works at the above codes…

```
using Plots, LaTeXStrings
using Luxor
gr()
let
f(x) = x*(sin(x^(2))+1
f'
gradient_line(f, x₀) = (x -> f(x₀) + f'(x₀)*(x-x₀))
default(markerstrokecolor = "white", linewidth = 2);
w, h = 600, 400
i = 1
plot(f, -3:0.1:5, label = L"f(x) = x \ * sin(x^{2}) + 1",
xlabel = "x", ylabel = "f(x)");
function frame(scene, i)
background("white"); sethue("green")
# translate near bottom right corner
# scatter([i], [f(i)], label = "", markersize = 5);
plot(gradient_line(f, i), -3:0.1:0.5, label = "", color = 2);
circle_marker_pos = getworldposition(Point([i], f[i]))
for k = 1:0.1:3
setfont("Georgia Bold", 73)
sethue("black")
text(string("x = $k"),
Point(O.x-83, O.y-108),
halign=:center)
end
i += 0.1
end
demo = Movie(600, 400, "needforspeedtangent")
animate(demo, [Scene(demo, frame, 1:360)], creategif=true)
end
```

**LoadError: syntax: missing comma or ) in argument list**

**Stacktrace:**

** [1] top-level scope**

** @ ~/LasthrimProjection/plot.jl:7**

** [2] include(fname::String)**

** @ Base.MainInclude ./client.jl:451**

** [3] top-level scope**

** @ REPL[1]:1**

**in expression starting at /home/browni/LasthrimProjection/plot.jl:7**