If `y=(x+sqrt(x^(2)+a^(2)))^(n)`, then prove that, `(dy)/(dx) =(ny)/( sqrt(x^(2)+a^(2)))`

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

If xy=a[y+sqrt(y^(2)-x^(2))] , prove that, x^(3)(dy)/(dx)=y^(2)(y+sqrt(y^(2)-x^(2)))

If y=(x)/(sqrt(1+x^(2))) , prove that, x^(3)(dy)/(dx)=y^(3) .

If y="("x+sqrt(x^(2)-1)")"^(m) , then prove that, (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+m^(2)y=0

Find (dy)/(dx) , when y=log(x+sqrt(x^(2)-a^(2)))

If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a) (n y)/(sqrt(x^2+a^2)) (b) -(n y)/(sqrt(x^2+a^2)) (c) (n x)/(sqrt(x^2+a^2)) (d) -(n x)/(sqrt(x^2+a^2))

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

If y = (x+ sqrt(1+x^2))^n then prove that (1+x^2)y_2+xy_1 = n^2y .

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

If log(x^2-y^2)/(x^2+Y^2)=a the prove that (dy/dx)=y/x