How do we find the answer of the derivative when we are not even given a point in the function? In almost all problems I came across of derivatives, we were just given the function(for ex-x3) and we were told to find the derivative of the function. As it is to my understanding, derivative is the slope of the tangent at a point. So if we are not given a point in the function, how will we find the derivative of the function?

When someone says to find the derivative of a function in the manner you speak of, they are wanting you to find the derivative at an arbitrary point. This ends up being another function. For example:
$f(x) = x^2$
We know that at any point $x$ the derivative is $2x$. Therefore the derivative is $f’(x) = 2x$. The evaluation of that function gives you the value of the derivative at $x$. You didn’t pick a value of $x$ so you just leave it as “$x$”.
