Percentage error in X

To determine the percentage error in X, we need to use the concept of partial differentiation. Let's differentiate X with respect to M, L, and T.

Partial differentiation with respect to M, L, and T

Partial differentiation of X with respect to M:
dX/dM = La^bT^-c

Partial differentiation of X with respect to L:
dX/dL = Ma^bT^-c

Partial differentiation of X with respect to T:
dX/dT = -McLa^bT^-c-1

Calculating percentage error

Using the formula for percentage error, we can find the percentage error in X due to the errors in M, L, and T.

Percentage error in X = ((dX/dM * alpha/M)^2 + (dX/dL * beta/L)^2 + (dX/dT * gamma/T)^2)^0.5 * 100%

Explanation of formula

The formula for percentage error in X takes into account the individual percentage errors in M, L, and T. The partial derivatives of X with respect to M, L, and T represent the sensitivity of X to changes in M, L, and T. By multiplying these partial derivatives with the percentage errors in M, L, and T, we get the percentage error in X due to each parameter.

The sum of the squares of these percentage errors is taken, and the square root of this sum is multiplied by 100% to get the final percentage error in X.

Conclusion

In summary, the percentage error in X can be calculated using partial differentiation and the formula for percentage error. The individual percentage errors in M, L, and T are multiplied by the sensitivity of X to changes in these parameters to get the percentage error in X due to each parameter. The sum of these percentage errors is taken, and the square root of the sum is multiplied by 100% to get the final percentage error in X.

∆x/x ×100=( a× alpha +b×beta +c×gamma)×100