Standard error for marginal effect in regression?

[annieta]

Hi,

I have a regular OLS regression that includes a variable both by itself and squared (i.e. y=b0+b1*x+b2*x^2). I am interested in the marginal effect of the variable at the mean. I know how to get the point estimate, but does anyone know how to get standard errors for the marginal effect? Many thanks!

Annie

 

[EnumaElish]

Define ME = b1 + 2*b2*x.

Var[ME] = Var[b1] + 4x^2 Var[b2] + 4x Cov[b1, b2] where x is treated as a constant (for example, x = the sample average).

Can you get to the standard error from here?