`y = sqrt(1 + x^(2)) : y' = (xy)/(1 + x^(2))`

(1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 when x= 1

If sin^(-1) x + sin^(-1) y + sin^(-1) z = pi" , prove that " x sqrt(1-x^(2) ) + y sqrt(1 - y^(2)) + zsqrt( 1 - z^(2)) = 2 xyz .

xy = log y + C : y' = (y^(2))/(1 - xy)(xy ne 1)

If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y) , then prove that (dy)/(dx)= sqrt((1-y^(2))/(1-x^(2))) . (Where |x| le 1, |y| le 1 )

y = x sin x : xy' = y + x sqrt(x^(2) - y^(2))(x ne 0 and x gt y or x lt -y)

If x^(2)+y^(2)+z^(2)-2xyz=1 , then the value of (dx)/(sqrt(1-x^(2)))+(dy)/(sqrt(1-y^(2)))+(dz)/(sqrt(1-z^(2))) is equal to………..

If sqrt(x^(2) + y^(2))=a. e^(tan^(-1)((y)/(x))), a gt 0 then the value of y''(0) is…….

If y= (tan^(-1) x)^(2) show that (x^(2) + 1)^(2) y_(2) + 2x (x^(2) + 1)y_(1) = 2

Verify (i) x ^(3) + y ^(3) = (x + y) (x ^(2) -xy + y ^(2)) (ii) x ^(3) -y ^(3) = (x-y) (x ^(2) +xy +y ^(2)) using some non-zone positive integers and check by actual multiplication. Can you call these as identities ?