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.
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