(d)/(dx)[tan^(-1)(log(e/x^(2)))/(log(ex^(2)))]

(d)/(dx)[tan^(-1)((log(ex))/(log(e//x)))]=(1)/(xf(x))," then "f(x)=

If y=tan^(-1)[(log(e//x^(3)))/(log(ex^(3)))]+tan^(-1)[(log(e^(4)x^(3)))/(log(e//x^(12)))]," then "(d^(2)y)/(dx^(2))=

d/(dx) (tan^(-1)((e^(2x)+1)/(e^(2x)-1)))=

(d)/(dx)[tan^(-1)((6x)/(1+7x^(2)))]+(d)/(dx)[tan^(-1)((5+2x)/(2-5x))]=

(d)/(dx)(log tan x)

(d)/(dx)[a tan^(-1)x+b log((x-1)/(x+1))]=(1)/(x^(4)-1)rArr a-2b=

(d)/(dx)[tan^(-1)(1+xsqrt(2))]+(d)/(dx)[tan^(-1)\(1-xsqrt(2))]=

(d)/(dx ) { (1)/( 6) log ""((x-1)^(2))/(x ^(2) + x +1 ) + (1)/( sqrt3)Tan ^(-1) ((2x +1)/( sqrt3))}=