A function `f: R rarr R" satisfies sin x cos y "(f(2x+2y)-f(2x-2y))= cos x sin y (f(2x+2y)+f(2x-2y)).`" If "f'(0)=(1)/(2),` then

A function f: R rarr R satisfies sin x cosy (f(2x2y))-f(2x-2y))= cosxsiny(f(2x+2y))+f(2x-2y)) If f'(0)=1/2 , then

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a)f^(prime)(x)=f(x)=0 (b)4f^(x)+f(x)=0 (c)f^(x)+f(x)=0 (d)4f^(x)-f(x)=0

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f''(x)=f(x)=0 (b) 4f''(x)+f(x)=0 (c) f''(x)+f(x)=0 (d) 4f''(x)-f(x)=0

A function f: RvecR satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n a)f^('')(x)=f(x)=0 b)4f^('')(x)+f(x)=0 c)f^('')(x)+f(x)=0 d)4f^('')(x)-f(x)=0

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then f'(x)=

A function f:R rarr R^(+) satisfies f(x+y)=f(x)f(y)AA x in R If f'(0)=2 then f'(x)=

A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for allx,y in R and f(x)!=0 for all x in R .If f(x) is differentiable at x=0 .If f(x)=2, then prove that f'(x)=2f(x) .

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)