Let #y=e^(ktan sqrt(3x)#
#d/dx (y)=d/dx (e^(ktan sqrt(3x)))#
#d/dx (y)=e^(ktan sqrt(3x))*d/dx (ktan sqrt(3x))#
#d/dx (y)=e^(ktan sqrt(3x))(k sec^2 sqrt(3x))*d/dx (sqrt(3x))#
#d/dx (y)=e^(ktan sqrt(3x))(k sec^2 sqrt(3x))* (1/sqrt(3x))*d/dx (3x)#
#d/dx (y)=e^(ktan sqrt(3x))(k sec^2 sqrt(3x))* (1/sqrt(3x))*3*d/dx (x)#
#d/dx (y)=e^(ktan sqrt(3x))(k sec^2 sqrt(3x))* (1/sqrt(3x))*3(1)#
#d/dx (y)=e^(ktan sqrt(3x))(k )(sec^2 sqrt(3x))* (1/sqrt(3x))*3(1)#
Simplification
#d/dx (y)=(3k)/(2sqrt(3x)) (sec^2 sqrt(3x))*e^(ktan sqrt(3x) )#
The final answer after some rationalization of radicals
#d/dx (y)=(k sqrt(3x))/(2x) *(sec^2 sqrt(3x))*e^(ktan sqrt(3x) )#
God bless...I hope the explanation is useful.