`"If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=`

Options

A. `x(dy)/(dx)-y`
B. `(x(dy)/(dx)-y)^(2)`
C. `y(dy)/(dx)-x`
D. `(y(dy)/(dx)-x)^(2)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Rewrite the function
Given:
\[ y = x \log\left(\frac{x}{a + bx}\right) \]

Using the property of logarithms:
\[ \log\left(\frac{x}{a + bx}\right) = \log(x) - \log(a + bx) \]
...