If `h(x)=x^(x^x),` then at `x=1,(h^(prime)(x))/(h(x))` is equal to

let f(x)=e^x ,g(x)=sin^(- 1) x and h(x)=f(g(x)) t h e n f i n d (h^(prime)(x))/(h(x))

If f(x)=x+1.g^(-1)(x)=x^(3)+x+1 and g(f(x))=h(x) then lim_(x rarr1)(h^(-1)(x)-h^(-1)(1))/(x-1) is equal to

If h (x) = e ^(e ^(x)) then (h '(x))/( h(x))

Let f be twice differentiable function such that f''(x)=-f(x) and f'(x)=g(x), h(x)={f(x)}^(2)+{g(x)}^(2) . If h(5) = 11, then h(10) is equal to :

let f(x) be differentiable at x=h then lim_(x rarr h)((x+h)f(x)-2hf(h))/(x-h) is equal to

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(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 the value of k is

If f is twice differentiable such that f^(')(x)=-f(x) and f^(prime)(x)=g(x)dot If h(x) is twice differentiable function such that h^(prime)(x)=(f(x))^2+(g(x))^2dot If h(0)=2,h(1)=4, then the equation y=h(x) represents (a)a curve of degree 2 (b)a curve passing through the origin (c)a straight line with slope 2 (d)a straight line with y intercept equal to 2.

If f(x) is a twice differentiable function such that f'' (x) =-f(x),f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) is equal to

If f(x) is a twice differentiable function such that f'' (x) =-f,f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) is equal to