(d)/(dx)(tan^(-1)sqrt(x))=

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(d)/(dx)[(tan sqrt(5x))] =

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

(d)/(dx) {Tan ^(-1) (sqrt(1+ x ^(2))-1)/( x)}=

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

If (d)/(dx)[cot^(-1)(x+1)]+(d)/(dx)(tan^(-1)x)=(d)/(dx)(tan^(-1)u)," then "u=

(d)/(dx)(tan^(-1)((x)/(sqrt(a^(2)-x^(2))))

(d)/(dx)[tan{tan^(-1)((x)/(a))-tan^(-1)((x-a)/(x+a))}]=

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

(d)/(dx)(tan^(-1)(sec x+tan x))=...