How can I find the tangent vector direction to a function \[y=x^3\]
I took the derivative of it and then I got this: \[y'=3x^2\] But this is just the equation to the gradient.
I am trying to find a vector in terms of x \[\begin{bmatrix}
x\\
y
\end{bmatrix}\] such that the vector gives the direction of the tangent vector. How do I do so?

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you want a vector [ x y] pointing in the direction of the tangent
let x= 1, and y= 3x^2
[1 3x^2]

Why is x=1? What is the reason for having x as 1?

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