" (wi) "tan^(-1)((x^(1/3)+a^(1/3))/(1-x^(1/3)a^(1/3)))

Differentiate the following w.r.t. x: tan^-1((x^(1//3)+A^(1//3))/(1-x^(1//3)a^(1//3)))

Differentiate tan^(-1){(x^(1//3)+a^(1//3))/(1-(a x)^(1//3))} with respect to x

Differentiate tan^(-1){(x^(1/3)+a^(1/3))/(1-(ax)^(1/3))} with respect to x]} with

tan^(-1)((3x-x^(3))/(1-3x^(2)))

Tan^(-1)((3x-x^(3))/(1-3x^(2)))=

tan^(-1)x+(tan^(-1)(2x))/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|<(1)/(sqrt(3))

Prove that: i) sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2 ii) cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1 iii) tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3) iv) tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))

int(x^(4)+1)/(x^(6)+1)dx(1)tan^(-1)x-tan^(-1)x^(3)+c(2)tan^(-1)x-(1)/(3)tan^(-1)x^(3)+c(3)tan^(-1)x+tan^(-1)x^(3)+c(4)tan^(-1)x+(1)/(3)tan^(-1)x^(3)+c

Prove that tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2)))absxlt(1)/(sqrt(3)).

If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y . Then which of the following may be true