Let f be a differentiable function such that `f(0)=e^(2)` and `f'(x)=2f(x)` for all `x in R`If `h(x)=f(f(x))` ,then `h'(0)` is equal to

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

Let f be a differentiable function defined on R such that f(0) = -3 . If f'(x) le 5 for all x then

Let f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

Let f:(0,oo)rarr R be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in(0,oo) and f(1)=1, then

Let f:R to R and h:R to R be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(g(x)))=x for all x in R . Then, h'(1) equals.

If f:R rarr R is a differentiable function such that f(x)>2f(x) for all x in R and f(0)=1, then

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0

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