I'm wanting to calculate the experimental uncertainty in the following function:

 

N = f(x,y) = a*exp(-x/y)

where a is a constant.

 

I've applied the following technique:

For z = f(x,y), Δz = sqrt[ (∂f/∂x * Δx)² + (∂f/∂y * Δy)² ]

 

And calculated:

ΔN = sqrt [ ( (-a/x)*exp(-x/y)*Δx )² + ( (ax/y²)*exp(-x/y)*Δy )² ]

 

However this is giving me an error far in excess of what I should be getting... can someone advise where I've gone wrong?

I think it's;

 

ΔN = sqrt [ ( (-a/y)*exp(-x/y)*Δx )² + ( (ax/y²)*exp(-x/y)*Δy )² ]