Geographic Meaning of Differentiation

Hello All,

The following is a paragraph from my book...

"Find the slope of the tangent to the curve at the point where . Find the angle at which this tangent makes with the curve . The slope of the tangent is the slope of the curve at the point where they touch one another; that is, it is the of the curve for that point. Here and for , which is the slope of the tangent and of the curve at that point. The tangent, being a straight line, has for equation , and its slope is , hence . Also, if , and as the tangent passes by this point, the coordinates of that point must satisfy the equation of the tangent, namely: so that and ; the equation of the tangent is therefore "

So here are my questions regarding this paragraph:

1.) When I take the tangent of the first curve, I get ...how does he come up with ?

(depending on the answer, I might have more questions to follow) Thanks.