Question

Find the derivative of g(x)=secx/(x+1)^3

Answer 1

Given data:

The given function is g(x)=secx/(x+1)^3.

The expression for the derivative of the function is,

`\begin{gathered} (d)/(dx)g(x)=(d)/(dx)(\sec x)/((x+1)^3) \\ \text{ =}((x+1)^3(d)/(dx)(\sec x)-\sec x(d)/(dx)(x+1)^3)/(\lbrace(x+1)^3\rbrace^2) \\ =(\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}`

Thus, the derivative of the giiven function is (secxtanx(x+1)-3sex)/(x+1)^4.