If `f(x)=(g(x)+g(-x))/2 + 2/[h(x)+h(-x)]^(-1),` where `g` and `h` are differentiable functions, then `f' (0)`

If f(x)=(g(x)+g(-x))/(2)+2/([h(x)+h(-x)]^(-1)) where g and h are differentiable functions then f""^(1)(0) =

Let F(x)=f(x)g(x)h(x) for all real x , where f(x),g(x) , and h(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0), and h^(prime)(x_0)=kh(x_0) . Then k is________

Let F(x) = f(x).g(x).h(x) x in R , where f(x) , g(x) & h(x) are differentiable function. At some point x_0, F'(x_0) = 21 F(x_0) , f'(x_0) = 4f(x_0),g'(x_0) = -7g(x_0), h'(x_0)= k.h(x_0) then k/4 =

Let f(x) = [x] , g(x)= |x| and f{g(x)} = h(x) ,where [.] is the greatest integer function . Then h(-1) is

Let f(x) = [x] , g(x)= |x| and f{g(x)} = h(x) ,where [.] is the greatest integer function . Then h(-1) is

If the three function f(x),g(x) and h(x) are such that h(x)=f(x)g(x) and f'(a)g'(x)=c , where c is a constant, then : (f''(x))/(f(x))+(g''(x))/(g(x))+(2c)/(f(x)f(x)) is equal to :