I'll do f_(xx), you can do the rest.

To get a partial derivative with respect to x, treat all other variables as constants. So given:

f = e^(4x) - sin(y^2) - sqrt(xy)

f_(x) = 4e^(4x) - (1/2)*(1/sqrt(xy))*y

f_(x) = 4e^(4x) - (1/2)sqrt(y/x)

To proceed it is simpler to look at this as:

f_(x) = 4e^(4x) - (1/2)sqrt(y)*x^(-1/2)

So:

f_(xx) = 16e^(4x) - (1/2)sqrt(y)*(-1/2)x^(-3/2)

Which is the same as:

f_(xx) = 16e^(4x) + (1/4)sqrt(y/x^3)

The other two are done the same way, though they require a bit more work.

-Dan