How do i find the equation of a tangent line to a curve given by a certain point

plz give me nicely WRITTEN steps. i would like written steps as so i can study the process for my upcoming test! thank you !

A lot depends on what information you are given.

Most questions will give you the tangent point (or the x-value of this point), as well as the equation of the curve.

If you are only given the x-value, the first step will be to find the y-value at that point.
To do so, just substitute the x-value into the equation.

The second step will be to differentiate the equation given.
This will give you the general equation for the slope at each point of the curve.

The third step will be to substitute the x-value of the point into the general equation of the slope.
This will allow you to find the slope at the tangent point.

The fourth step will be to apply the slope formula to find the tangent line.
Suppose the tangent point is (a, b), and the slope which you found is c.
By the slope formula, the tangent line will be: (y - b) / (x - a) = c.