# Guide to Calculus Derivatives

### From BluWiki

- Calculus evolved from several problems facing mathematics during the seventeeth century. One such problem was to find a line that is tangent to a curve at a specific point. While this is easily geometrically defined for circles (the line touching the circle at exactly one point
*P*) it does not provide a general solution for all curves. The problem boils down to finding the slope of the tangent at point*P*.

## Definition of a Derivative

- By understanding the limit, it is easy to see that the two points (x,f(x)) and (x+h,f(x+h)) will become infinitely close as <math>h->0</math>, because h is becoming infinitely small. Slope is given as the change in <math>y</math> over the change in <math>x</math>. The change in <math>y</math> is <math>f(x+h)-f(x)</math>. The change in <math>x</math> is <math>(x+h)-x</math>, or <math>h</math>.

Derivatives do not exist in certain situations. If at a value of x there is a hole, discontinuity, jump, asymptote, vertical tangent, or a sharp turn in the graph a derivative does not exist at that point.