Question

Differentiate function Y=Ln^2(2x+11)

Answer 1

Answer:

$\frac{\textbf{dy}}{\textbf{dx}}=\frac{\textbf{2}}{\textbf{x}}+\frac{\textbf{4}}{\textbf{11}}$

Step-by-step explanation:

Given function is

$y=\log^2(2x+11)$

the above function can be written as

$y=2\log(2x+11)$

(By using the formula $\log x^n =n \log x$)

Now differentiate the above function with respect to x on both sides

$\frac{dy}{dx}=2\left[\frac{1}{2x+11}\right]\ (2)$  

(By using formula $\log x=\frac{1}{x}$ and $\log (ax+b)=\left(\frac{1}{ax+b}\right){(a)}=\frac{a}{ax+b}$ where a and b constants)

    $=\frac{4}{2x+11}$

    $=\frac{4}{2x}+\frac{4}{11}$

Therefore

$\frac{dy}{dx}=\frac{2}{x}+\frac{4}{11}$