If ` ysqrt(1-x^(2)) +xsqrt( 1-y^(2)) =1,then (dy)/(dx)=`

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

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

If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(dx) - (2x)/(sqrt(1 - x^4)) = 1/(sqrt(1 - x^2))

If f'(x)= sqrt(2x^(2)-1) and y=f(x^(2)),then (dy)/(dx) at x = 1 is

If xsqrt(1 + y) + ysqrt(1 + x) = 0 show that (dy)/(dx) = - 1/(1 + x)^2

If y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1-x^2))] find dy/dx

If ysqrt(x^(2)+1)=log(x+sqrt(x^(2)+1)) , show that (x^(2)+1)(dy)/(dx)+xy-1=0 .

Statement I The ratio of length of tangent to length of normal is proportional to the ordinate of the point of tangency at the curve y^(2)=4ax . Statement II Length of normal and tangent to a curve y=f(x)" is "|ysqrt(1+m^(2))| and |(ysqrt(1+m^(2)))/(m)| , where m=(dy)/(dx).

If log (sqrt(1 + x^2) - x) = y sqrt(1 + x^2) , show that (1 - x^2) (dy)/(dx) + xy + 1 = 0