Given that `f(x,y)=x^(3)y`. Find `f_(xy)`
(A) `2xy`
(B) `x^(2)`
(C) `3x^(2)`
(D) None of these

Given the function f(x)=(a^(x)+a^(-x))/(2)(wherea>2)dot Then f(x+y)+f(x-y)= (A) 2f(x).f(y) (B) f(x).f(y) (C) (f(x))/(f(y)) (D) none of these

The differential equation of all conics whose centre klies at origin, is given by (a) (3xy_(2)+x^(2)y_(3))(y-xy_(1))=3xy_(2)(y-xy_(1)-x^(2)y_(2)) (b) (3xy_(1)+x^(2)y_(2))(y_(1)-xy_(3))=3xy_(1)(y-xy_(2)-x^(2)y_(3)) ( c ) (3xy_(2)+x^(2)y_(3))(y_(1)-xy)=3xy_(1)(y-xy_(1)-x^(2)y_(2)) (d) None of these

Let f(x)=|x-1|* Then (a) f(x^(2))=(f(x))^(2) (b) f(x+y)=f(x)+f(y)(c)f(|x|)-|f(x)| (d) none of these

If y=(log)_(e)((x)/(a+bx))^(x), then x^(3)y_(2)=(xy_(1)-y)^(2)(b)(1+y)^(2)(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these

If f(x+y,x -y)= xy then (f(x,y)+f(y,x))/(2)=

If f(x+2y,x-2y)=xy, then f(x,y) equals

The differential equations of all circle touching the x-axis at orgin is (a) (y^(2)-x^(2))=2xy((dy)/(dx)) (b) (x^(2)-y^(2))(dy)/(dx)=2xy ( c ) (x^(2)-y^(2))=2xy((dy)/(dx)) (d) None of these

If y=(log)_(e)((x)/(a))^(x), thenx ^(3)y_(2)=b)(xy_(1)-y)^(2).(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these

The length of a rectangle is y xx its breadth x .The area of the rectangle is: xy(b)xy^(2)(c)x^(2)y(d) None of these

Find f(x, y) if f(x + 2y, 2x + y) = 2xy.