If `f(2x+3y, 2x-7y)=20x,` then `f(x,y)` equals :

Let f:R to R be a function satisfying f(x+y)=f(x)=lambdaxy+3x^(2)y^(2)"for all "x,y in R If f(3)=4 and f(5)=52, then f'(x) is equal to

A function f:RtoR is such that f(x+y)=f(x).f(y) for all x.y inR and f(x)ne0 for all x inR . If f'(0)=2 then f'(x) is equal to

If f(x,y) =e^(xy) , then (del^(2)f)/(del x del y) is equal to

If f(x, y)=(max (x, y))^(min (x, y)) and g(x, y)=max (x, y) -min (x, y) , then f(g(-1,(-3)/(2)), g(-4,-1.75)) equals

y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)) , AAx,y->R and f'(0)=0.Then f(6)is equal ______

If f(x,y) =x^(3) + y^(3) -3xy^(2) , then (del f)/(del x) at x=2, y=3 is

Let f be a differentiable function from R to R such that abs(f(x)-f(y))abs(le2)abs(x-y)^(3//2) ,for all x,y inR .If f(0)=1 ,then int_(0)^(1)f^2(x)dx is equal to

f(x+y)=f(x).f(y) for all x,yinR and f(5)=2,f'(0)=3 then f'(5) is equal to