Im studying for a final and I just need some reassurance.

1. Find the directional derivative of $\displaystyle f(x,y)=x^2+y^2+1 at (1,2) in the direction from (1,2) to (3,6)$

I found partial derivatives, found the direction vector, found the unit vector, My answer is $\displaystyle 16/sqrt (5)$

2.Find the area of the surface $\displaystyle z=16-x^2-y^2$ over the region $\displaystyle {(x,y)|x^2+y^2=16} $

I setup double integral using polar coordinates, r from 0 to 4, theta from 0 to 2pi.

My final answer is 256pi/3.