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

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

(d)/(dx)(tan^(-1)((sqrt(x)-x)/(1+x^((3)/(2))))) equals- (x<=0)

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

(d)/(dx)[sec(tan^(-1)x)]=

(d)/(dx)[log(sec x+tan x)]=

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

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

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

(d)/(dx)tan^(-1)((sqrt(x)-x)/(1+x^((3)/(2))))=

(d)/(dx)(tan^(-1)(birth x))