|(1-sqrt(x)dr t)

The solution for x of the equation int_(sqrt2)^(x)(dt)//t(sqrt(t^(2)-1))=(pi)/(2) is

Differentiate tan^(-1)[(sqrt(x)+sqrt(a))/(1-sqrt(ax))] w.r.t. x.

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t)) and tan (y/2)=sqrt((1-t)/(1+t)) then (dy)/dx at t=1/2 is

e^(x)=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t)) andtan (y)/(2)=sqrt((1-t)/(1+t)) then (dy)/(dx) at t=(1)/(2) is (a)-(1)/(2) (b) (1)/(2)(c)0(d) none of these

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a n dtany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

The slopee of normal to the curve x=sqrt(t) and y=t-(1)/(sqrt(t)) at t=4 is . . .

Derivatives sin^(-1) ((sqrt(1+x)+sqrt(1-x))/2) w.r.t cos^(-1)x is

If y=sqrt(x)+1/(sqrt(x)),p rov et h a t2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)] prove tha t dy/dx is (1)/(2sqrt(x(1-x)))