Write the following function in the simplest form: `tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))`

Write the following function in the simplest form: tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2))),a>0;(-a)/(sqrt(3))<=x<=(a)/(sqrt(3))

Write the following functions in the simplest form: tan^(-1){(x)/(sqrt(a^(2)-x^(2)))}

Write the following function in the simplest form: tan^(-1)((sqrt(1+x^(2))-1)/(x)),x!=0

Write the following function in the simplest form: (tan^(-1)x)/(sqrt(a^(2)-x^(2))),|x|

Write the following function in the simplest form: tan^(-1)((1)/(sqrt(x^(2)-1))),|x|>1

Differentiate tan^(-1)((3x-x^(3))/(1-3x^(2))), if x>(1)/(sqrt(3))

Differentiate tan^(-1)((3x-x^(3))/(1-3x^(2))), if -1/(sqrt(3))

Write the following functions in the simplest form: (i) tan^(-1){x/(sqrt(a^2-x^2))},\ -a< x < a (ii) tan^(-1){sqrt((a-x)/(a+x))},\ -a< x < a

Write the following functions in the simplest form: sin^(-1){(x)/(sqrt(x^(2)+a^(2)))}( ii) cos^(-1){(x)/(sqrt(x^(2)+a^(2)))}

y=tan^(-1)""(3x-x^(3))/(2x^(2)-1),-(1)/(sqrt(3))ltxlt(1)/(sqrt(3))