Question

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

Answer 1

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

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

`(dy)/(dx)=2\left[(1)/(2x+11)\right]\ (2)`

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

`=(4)/(2x+11)`

`=(4)/(2x)+(4)/(11)`

Therefore

`(dy)/(dx)=(2)/(x)+(4)/(11)`