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

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

If y = (sinh^(-1)x)/(sqrt(1 + x^(2)))"then" (1 +x^(2) ) y_(2) + 3xy_(1)+ y =

If y=(sinh^(-1)x)/(sqrt(1+x^(2))) then (1+x^(2))y_(2)+3xy_(1)=

If y=(sin^(-1)x)/(sqrt(1-x^(2))), then ((1-x^(2))dy)/(dx) is equal to x+y (b) 1+xy1-xy(d)xy-2

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

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

Prove that sin ^ (- 1) x + cos ^ (- 1) y = (tan ^ (- 1) (xy + sqrt ((1-x ^ (2)) (1-y ^ (2)))) ) / (y sqrt (1-x ^ (2)) - x sqrt (1-y ^ (2)))

If y^(1/m)= x + sqrt (1 + x^(2)) "then" (1 + x^(2))y_(2)+ xy _(1) = ?

Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b) (x+sqrt(x^2-1))/(x-sqrt(x^(2)-1)) -(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

If y sqrt(1+ x ^(2)) = log ( x + sqrt( 1 + x ^(2))) then (1 + x ^(2)) y_(1) + xy=