Answer :
Given data:
The given function is g(x)=secx/(x+1)^3.
The expression for the derivative of the function is,
[tex]\begin{gathered} \frac{d}{dx}g(x)=\frac{d}{dx}\frac{\sec x}{(x+1)^3} \\ \text{ =}\frac{(x+1)^3\frac{d}{dx}(\sec x)-\sec x\frac{d}{dx}(x+1)^3}{\lbrace(x+1)^3\rbrace^2} \\ =\frac{\sec x\tan x(x+1)^3-3(x+1)^2\sec x}{(x+1)^6} \\ =\frac{(x+1)^2\lbrace\sec x\tan x(x+1)^{}-3^{}\sec x\rbrace}{(x+1)^6} \\ =\frac{\sec x\tan x(x+1)^{}-3^{}\sec x}{(x+1)^4} \\ \\ \end{gathered}[/tex]Thus, the derivative of the giiven function is (secxtanx(x+1)-3sex)/(x+1)^4.