If `f(x,y)=2x^(2)-xy+2y^(2)` then find `f_x` at the point `(1,2)`

If f'(x)=sqrt(2x^(2)-1) and y=f(x^(2)), then find (dy)/(dx) at x=1

Let f(x,y)=x^(2)+2xy+3y^(2)-6x-2y, where x, y in R, then

If f(x)=(2^(x)+2^(-x))/(2), then f(x+y)f(x-y) is equals to (1)/(2){f(2x)+f(2y)}(b)(1)/(2){f(2x)-f(2y)}(c)(1)/(4){f(2x)+f(2y)}(1)/(4){f(2x)-f(2y)}

Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -(g (x,y))^(2)=1/2 and f (x,y) . G(x,y) =(sqrt3)/(4) Find the number of ordered pairs (x,y) ?

If x^(2) + y^(2) = 12 xy , then find the value of (x^(2))/(y^(2)) + (y^(2))/(x^(2)) .

The straight line y=2x meets y=f(x) at P, where f(x) is a solution of the differential equation (dy)/(dx)=(x^(2)+xy)/(x^(2)+y^(2)) such that f(1)=3 , then f'(x) at point P is