If `f,g,a n dh` are differentiable functions of `xa n d(x)=|fgh(xf)'(xg)'(x h)'(x^(f2)f)' '(x^2g)' '(x^2h)' '|` prove that `^(prime)=|fgff'g' h '(x^3f' ')'(x^3g' ')'(x^3h ' ')'|`

Let f,g, h be differentiable functions of x. if Delta = |(f,g,h),((xf)',(xg)',(xh)'),((x^(2) f)'',(x^(2)g)'',(x^(2) h)'')|and, Delta' = |(f,g,h),(f',g',h'),((x^(n)f'')',(x^(n) g'')',(x^(n) h'')')| , then n =

If f(x) is a differentiable function of x then lim_(h rarr0)(f(x+3h)-f(x-2h))/(h)=

Let f be a twice differentiable function such that f''(x)=-f(x), and f'(x)=g(x),h(x)=[f(x)]^(2)+[g(x)]^(2) Find h(10) if h(5)=11

Let f and g be two differential functions such that f(x)=g'(1)sin x+(g''(2)-1)xg(x)=x^(2)-f'((pi)/(2))x+f''((-pi)/(2))

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

If f(x) and g(x) are non- periodic functions, then h(x)=f(g(x))is

Let f be a twice differentiable function such that f''(x)=-f(x)" and "f'(x)=g(x)."If "h'(x)=[f(x)]^(2)+[g(x)]^(2), h(a)=8" and "h(0)=2," then "h(2)=

If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is