[" 4."y=sqrt(1+x^(2))," : "y'=(xy)/(1+x^(2))]

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

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

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) = ?

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

If cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^(-1)y=4sec^(-1)z+5cos ec^(-1)z, then prove that sqrt(z^(2)-1)=(sqrt(1+x^(2))-xy)/(x+y sqrt(1-x^(2)))

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

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