Page 262 - Well Logging and Formation Evaluation
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252 Well Logging and Formation Evaluation
y
a
1
b
x
Figure A4.1 Equation of a Straight Line
Table A4.1
Function dy/dx
n
y = x + a (n π 0) n*x n-1
y = e x e x
y = log(x) (log is natural logarithm base e) 1/x
y = sin(x) (x must be in radians = deg*p/180) cos(x)
y = cos(x) (x must be in radians = deg*p/180) -sin(x)
2
y = tan(x) sec (x) (sec = 1/cos)
x
y = a x a *log(a)
on more than one input variable, the situation is a bit more complex. Con-
sider the function:
+
t = a x b y
*
*
In order to derive dt/dx you also need to know how y will vary with x,
if at all. In most engineering applications, x and y might be parameters
such as pressure or temperature, which one can control in a laboratory. A
special notation convention is used when the differential with respect to
one variable is derived while keeping the other variables constant. Hence
the partial differential of t with respect to x while keeping y constant is
denoted as ∂t/∂x, or sometimes ∂t/∂x| y.