Answer:
[tex]\frac{\textbf{dy}}{\textbf{dx}}=\frac{\textbf{2}}{\textbf{x}}+\frac{\textbf{4}}{\textbf{11}}[/tex]
Step-by-step explanation:
Given function is
[tex] y=\log^2(2x+11)[/tex]
the above function can be written as
[tex] y=2\log(2x+11)[/tex]
(By using the formula [tex] \log x^n =n \log x[/tex])
Now differentiate the above function with respect to x on both sides
[tex]\frac{dy}{dx}=2\left[\frac{1}{2x+11}\right]\ (2)[/tex]
(By using formula [tex]\log x=\frac{1}{x}[/tex] and [tex]\log (ax+b)=\left(\frac{1}{ax+b}\right){(a)}=\frac{a}{ax+b}[/tex] where a and b constants)
[tex]=\frac{4}{2x+11}[/tex]
[tex]=\frac{4}{2x}+\frac{4}{11}[/tex]
Therefore
[tex]\frac{dy}{dx}=\frac{2}{x}+\frac{4}{11}[/tex]
