Question

a)find the first partial derivatives of f(x y)= x √1+y^2

b)find the first partial derivatives of f(x,y)= e^x ln y at the point (0,e)

Answer 1

f(x,y) = x√(1+y^2)
fx = (√1+y^2)
fy = xy/(√1+y^2)

Just treat the other variables as constants.

Answer 2

fx=e^xlny
fy=e^x/y

fx=e^(0)ln(e)=1
fy=1/e