tan^(-1)((sqrt(1+a^(2)*x^(2)-1))/(ax))_(" frece "^(2))=(1)/(2)tan^(-1)ax

Differentiate w.r.t. as indicated : tan^(-1)((sqrt(1+a^(2)x^(2))-1)/(ax))" w.r.t. "tan^(-1)ax

tan^(-1)((sqrt(1+a^(2)x^(2))-1)/(ax)) where x!=0, is

tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

tan^(-1)((a-x)/(1+ax))

IfI=int(dx)/(x^(3)sqrt(x^(2)-1)), then Iequals a.(1)/(2)((sqrt(x^(2)-1))/(x^(3))+tan^(-1)sqrt(x^(2)-1))+C b.(1)/(2)((sqrt(x^(2)-1))/(x^(2))+x tan^(-1)sqrt(x^(2)-1))+Cc(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+Cd(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+C

11Ify=tan^(-1)[(sqrt(1+a^(2)x^(2))-1)/(ax)],thenfind(dy)/(dx)

If y=tan^(-1)[(sqrt(1+a^(2)x^(2))-1)/(ax)] , then find (dy)/(dx) .

tan^-1 [(1)/(sqrt(x^2-1))]

y = "tan"^(-1)((sqrt(1 + a^2x^2 ) - 1)/(ax)) implies (1 + a^2x^2)y^('') + 2a^2 xy^' =