Applying the product rule and the chain rule, we get
d s d z = d d z ( z 2 tan x z ) = ( z 2 ) ′ tan ( x z ) + z 2 d d z tan x z = 2 z tan ( x z ) + z 2 sec 2 ( x z ) d d z ( x z ) = 2 z tan ( x z ) + x z 2 sec 2 ( x z ) {\displaystyle {\frac {ds}{dz}}={\frac {d}{dz}}(z^{2}\tan xz)=(z^{2})'\tan(xz)+z^{2}{\frac {d}{dz}}\tan xz=2z\tan(xz)+z^{2}\sec ^{2}(xz){\frac {d}{dz}}(xz)=\color {blue}2z\tan(xz)+xz^{2}\sec ^{2}(xz)} .
.
