Use this formula to calculate:

Var(aX+bY) = { (a^2)*Var(X) } + { (b^2)*Var(Y) } + { (2ab)*Cov(X,Y) }

"Cov" denotes covariance here.

You might need to use the formula accordingly (or, modify) to suit your needs.

mean(Y)=a.mean(X1)+b.mean(X2)+c.mean(X3). IF X1, X2 and X3 are independent, then variance(Y)=a2.variance(X1)+b2.variance(X2)+c2.variance(X3). If they are dependent, there is no general relationship.

@ David, could please check your formula?

thanks.

if we have a function like Y=(aX1X2)/(X3+tan(X4)), how can calculate variance?

Is your question related to uncertainty in indirect measurements or is it more general, i.e. belonging to statistics?

In the first case you should easily find a formula estimating the variance of compound formula (function) when the variances (or standard deviations) of its components are known.  It is based on Taylor expansion of the function under investigation, with respect to its all variable arguments.  More precisely:

delta f(x1, x2, xN) = df/dx1 * delta x1 + ... + df/dxN * delta xN + higher order terms (neglected, as individual "errors" delta xk are assumed "small").  To operate with variances you need to compute squares of both sides.  Then we have:  Var(f) = sumk [(df/dxk)2 * Var(xk)} + terms containing products of first derivatives.

Replacing (df/dxi*df/dxk) * (delta xi * delta xk) with their absolute valus we obtain upper estimate of Var(f).

Var(Y)=Var(aX1)+Var(bX2)+Var(cX3)=(a*2)Var(X1)+(b*2)Var(X2)+(c*2)Var(X3)

Thanks for all especially Marek Wojciech Gutowski for answers.