If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+...... tooo))),p rov et h a t(dy)/(dx)=(cosx)/(2y-1)`

If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+oo)))),t h e np rov et h a t(dy)/(dx)=(y^2-x)/(2y^3-2x y-1)

If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s (a) x/(2y-1) (b) x/(2y+1) (c) 1/(x(2y-1)) (d) 1/(x(1-2y))

int (cosx)/(sqrt(2+sinx))dx

If int_0^ycost^2dt=int_0^(x^2)(sint)/t dx ,t h ep rov et h a t(dy)/(dx)=(2sinx^2)/(xcosy^2)

(dy)/(dx)+(y)/(x)=sinx

If y=sqrt(sinx+y),then (dy)/(dx)dot

If x=sqrt(a^(sin^(-1)t)), y= sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)= -(y)/(x) .

If y=sqrt(x+1)+sqrt(x-1) , prove that sqrt(x^(2)-1)(dy)/(dx)=1/2y

int sqrt(1-sinx)dx " is equal to "

Evaluate int cos^(3)x sqrt(sinx)dx .