Determining Standard Deviation of product given SD's of components

Hi,

Imagine two stocks A and B with known standard deviations and the correlation between them.

Another stock, say, an index C, is composed of 60% of A and 40% of B. What is the standard deviation of this index?

I have used the following forumla:

Covariance of A and B = correlation * SD of A * SD of B

Variance of C = .6 * (variance of A) + .4 * (variance of B) * 2 * .4 * .6 (covariance)

Then I square root the variance of C for the std dev. Is this right?

Thanks in advance.