find the derivative of y with respect to x.\n\n$y = 2 ln left( \frac { 8 } { x } \right)$\n\n$\frac { d y }…

find the derivative of y with respect to x.\n\n$y = 2 ln left( \frac { 8 } { x } \right)$\n\n$\frac { d y } { d x } = square$

find the derivative of y with respect to x.\n\n$y = 2 ln left( \frac { 8 } { x } \right)$\n\n$\frac { d y } { d x } = square$

Answer

Explanation:

Step1: Simplify the function

Use the logarithm property (\ln\frac{a}{b}=\ln a-\ln b). So (y = 2\ln8-2\ln x). Since (\ln8) is a constant, the derivative of (2\ln8) with respect to (x) is (0). Now we only need to find the derivative of (- 2\ln x).

Step2: Apply the derivative formula

The derivative of (\ln x) with respect to (x) is (\frac{1}{x}). Using the constant - multiple rule ((cf(x))^\prime = cf^\prime(x)) (where (c=-2) and (f(x)=\ln x)), we have ((-2\ln x)^\prime=-2\times\frac{1}{x}).

Answer:

(-\frac{2}{x})