Find `f(x)`, when `f^(prime)(x) = tanx/(1+2 tan^2 x)` and `f(pi/2)=sqrt(2)+log(sqrt(2))`.

Find f(x), when f'(x)=(tan x)/(1+2tan^(2)x) and f((pi)/(2))=sqrt(2)+log(sqrt(2))

f(x)=(tanx)/(sqrt(1+tan^(2)x)) and f((pi)/(2)-)=a,f((pi)/(2)+)=b then

If f is a real function such that f(x) > 0,f^(prime)(x) is continuous for all real x and a xf^(prime)(x)geq2sqrt(f(x))-2af(x),(a x!=2), show that sqrt(f(x))geq(sqrt(f(1)))/x ,xgeq1 .

If f is a real function such that f(x) > 0,f^(prime)(x) is continuous for all real x and a xf^(prime)(x)geq2sqrt(f(x))-2af(x),(a x!=2), show that sqrt(f(x))geq(sqrt(f(1)))/x ,xgeq1 .

Let f(x) = tan x, x in (-pi/2,pi/2)and g(x) = sqrt(1-x^2) then g(f(x)) is

If f is a real function such that f(x)>0,f^(prime)(xx) is continuous for all real xa n da xf^(prime)(x)geq2sqrt(f(x))-2af(x),(a x!=2), show that sqrt(f(x))geq(sqrt(f(1)))/x ,xgeq1.

Let f(x)=tanx, -pi/2 and g(x)= sqrt(1-x^2) . Describe gof.

Find f'(x), if f(x)= tan^(-1) ""sqrt((1-cos2x)/(1+cos2x))

f(x)=tan x,x in(-(pi)/(2),(pi)/(2)) and g(x)=sqrt(1-x^(2)) then g(f(x)) is

If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2) , then find (dy)/(dx) at x=1 .