Let f(x) be a differentiable function such that
`f'(x)=sinx+sin4xcosx.` Then `f'(2x^(2)+(pi)/(2))"at "x=sqrt((pi)/(2))` is equal to

If f'(x)=sinx+sin4x.cosx, then f'(2x^(2)+pi/2) is

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(x) be a differentiable function and f'(4)=5 . Then lim_(x to 2) (f(4) -f(x^(2)))/(x-2) equals

LEt f(x) be a differentiable function and f'(4)=5. Then,lim_(x rarr2)(f(4)-f(x^(2)))/(x-2) 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)) If phi (x) =f ^(-1) (x) then phi'((pi)/(2) +1) equals to :

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)) If phi (x) =f ^(-1) (x) then phi'((pi)/(2) +1) equals to :

If f(x)=(2-3cosx)/(sinx) , then f'((pi)/(4)) is equal to

Let f:(0,pi) rarr R be a twice differentiable function such that lim_(t rarr x) (f(x)sint-f(t)sinx)/(t-x) = sin^(2) x for all x in (0,pi) . If f((pi)/(6))=(-(pi)/(12)) then which of the following statement (s) is (are) TRUE?