Simplifying Uncertainty in g: Using Derivatives to Solve for Δg

[J-NCF]

Homework Statement

Okay so here's the background.

g=(4pi^2/T^2)l

The instructions are:
Estimate the uncertainty in g using the uncertainty propagation for a general function. The specific formula you should obtain for delta g is:

#1 Δg= g (sqrt(Δl/l)^2 + (2 ΔT/T)^2)

The uncertainty equation is :

#2 ΔF=(sqrt (partial derivative of x)^2( Δx)^2 + (partial derivative of y)^2( Δy)^2)

So basically, make equation #2 look like #1, and solve for delta g.

So the question is, how do I simplify equation #2 to look like equation #1.

F=g , x=l, and y=T is those equations.

Homework Equations

g=(4pi^2/T^2)l

#1 Δg= g (sqrt(Δl/l)^2 + (2 ΔT/T)^2)

#2 ΔF=(sqrt (partial derivative of x)^2( Δx)^2 + (partial derivative of y)^2( Δy)^2)

The Attempt at a Solution

I know the derivatives of g in relation to l and T. The professor said something about using the derivatives and replacing g into the second equation, then factoring that g out, which is how equation #1 has a g in front of the square root. I can do that with the derivative of T, however I am left with a -2 instead of a positive 2. I am missing a l for the deriative of l (obviously), so I don't really know where to go from there.

 

[tms]

Show what you have done. It may be that you have made a simple algebra mistake, but no one can tell for sure without seeing what you have done. It may also be that by writing out everything explicitly you will see your error.