Uncertainty Formula - Numbers

Formula:


For Arithmetic Operations

z = x + y   ,   dz = √((dx)2+(dy)2))
z = x - y   ,   dz = √((dx)2+(dy)2))
z = x * y   ,   dz = z * √((dx/x)2+(dy/y)2))
z = x / y   ,   dz = z * √((dx/x)2+(dy/y)2))

For Other Operations

z = x ^ y    ,   dz = z * √(dy * dy * log(x) * log (x) + ((y*dx)/x)2)
z = 1 /x     ,    dz = (dx / x)
z = ln(x)    ,   dz= log(e) * (dx/ x)
z = 10 ^ y   ,  dz = z * (dx * log(10))


Where,

z = Uncertainity Value
dz = Value of dz
x = Value of x
y = Value of y
dx = Value of dx
dy = Value of dy

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