Answer
Gradient of f i.e. grad f = i + j and equation of level curve is
x^2 + y^2 = 2.
Work Step by Step
In order to find the partial derivative we differentiate with respect to x keeping y as constant. Similarly it can be done for y by keeping x as constant.
fx(1,1)= (del by del x )ln(x^{2}+y^{2}) = 2x/(x^2+y^2).
Now putting (1,1) we get f_{x}=1.
Ft(1,1)=(del/(del x))ln(x^{2}+y^{2}) = 2x/(x^2+y^2).
Now putting (1,1) we get f_{y}=1.
Therefore, Gradient of f = i + j.
Now in order to find level curve we just have to put point (1,1) in the above equation.
ln(x^2+y^2) = ln(1+1) = ln(2).
Therefore, ln(x^2+y^2) = ln2 or simply
x^2 + y^2 = 2.
