Let f and g be differentiable functions on `R` such that `g(1)=3=g'(1)` and `f'(4)=(1)/(18-pi)` .If `h(x)=f(3x g(x)+sin(pi x)-5)` then `h'(1)` is equal to

Let f and g be differrntiable functions on R (the set of all real numbers) such that g (1)=2=g '(1) and f'(0) =4. If h (x)= f (2xg (x)+ cos pi x-3) then h'(1) is equal to:

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))

Let f be twice differentiable function such that g'(x)=-(f(x))/(g(x)),f'(x)=(g(x))/(f(x))h(x)=e^((f(x))^(2)+(g(x))^(2)+x)If h(5)=e^(6) then h(10) is equal to

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

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)."If "h'(x)=[f(x)]^(2)+[g(x)]^(2), h(a)=8" and "h(0)=2," then "h(2)=

Let f(x) and g(x) be the differentiable functions for 1<=x<=3 such that f(1)=2=g(1) and f(3)=10 .Let there exist exactly one real number c in(1,3) such that 3f'(c)=g'(c) ,then the value of g(3) must be

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.

Let f and g be two differentiable functins such that: f (x)=g '(1) sin x+ (g'' (2) -1) x g (x) = x^(2) -f'((pi)/(2)) x+ f'(-(pi)/(2)) The number of solution (s) of the equation f (x) = g (x) is/are :