Find the first partial derivatives?

Question

Find the first partial derivatives of the function at the given point.
help appreciated!
a. g(x,y) = sqrt(x^2+y^2) ; (3,4)

b.f(x,y) = e^xy (e to the xy) ; (1,1)

Answer 1

a.
∂g/∂x = x/sqrt(x^2+y^2) = 3/5 at (3,4)
∂g/∂y = y/sqrt(x^2+y^2) = 4/5 at (3,4)

b.
∂f/∂x = ye^xy = e at (1,1)
∂f/∂y = xe^xy = e at (1,1)

Answer 2

a. dg/dx = x/sqrt(x^2+y^2) eval at (3,4) get 3/sqrt(9+16) = 3/5

dg/dy = y/sqrt(x^2+y^2) eval ---> 4/5

b, df/dx = ye^xy eval at (1,1) = 1e^1
df/dy = xe^xy eval ---> 1e^1