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4vir4ik [10]
3 years ago
10

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

Mathematics
1 answer:
Studentka2010 [4]3 years ago
7 0

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}

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