Suppose a variable y depends on n independent variables x1, x2, x3,...,xn. If the independent variables have uncertainty Deltax1, Deltax2, etc. and the uncertainties are independent, then the uncertainty in y can be estimated with
Deltay = sqrt(sum((dy/dxj Deltaxj)^2))
For this problem, the relationship between y and xj will be power laws of the form
y = c x1^a1 x2^a2 x3^a3 ...xn^an
For example, the relationship KE = (1/2)mv^2 would have c = 0.5 and a = [1 2].
Write a function that takes a vector of values of x, the coefficient c, exponents a, and a vector of uncertainties Deltax and returns the absolute uncertainty Deltay, relative uncertainty Deltay/y, and the index of the variable that contributes the most to the uncertainty in y. Identifying the largest contributor to the uncertainty tells the experimentalist which measurement to target first to improve the measurement.
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