Page 46 - Standard Handbook Of Petroleum & Natural Gas Engineering

Differential and Integral Calculus 35

Figure 1-31. The polar plane.

radians. The origin is called the pole, and points [r,0] are plotted by moving
a positive or negative distance r horizontally from the pole, and through an
angle 0 from the horizontal. See Figure 1-31 with 0 given in radians as used in
calculus. Also note that
[r, 01 = [-r,e + n]

DIFFERENTIAL AND INTEGRAL CALCULUS
See References 1 and 5-8 for additional information.

Derivatives
Geometrically, the derivative of y = f(x) at any value xn is the slope of a
tangent line T intersecting the curve at the point P(x,y). Two conditions applying
to differentiation (the process of determining the derivatives of a function) are:
1. The primary (necessary and sufficient) condition is that

lim AY
AXXOO,
exists and is independent of the way in which Ax+O
2. A secondary (necessary, not sufficient) condition is that

lim Of(x+Ax) = f(x)
~
A short table of derivatives will be found in Table 1-6.