How do you differentiate and find the tangent?

Answer 1

When you differentiate a function, you find the slope of the function. The slope is also known as the tangent.

The slope of a line, given one point, and a second point relative to the first point, but with x different, is given as delta y over delta x.

Differentiation is simply taking the limit of the slope, i.e. where delta x approaches zero.