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 } = )

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 } = )

Answer

Explanation:

Step1: Use logarithm property

Use $\ln(\frac{a}{b})=\ln a-\ln b$. So $y = 2(\ln8-\ln x)=2\ln8 - 2\ln x$.

Step2: Differentiate term - by - term

The derivative of a constant ($2\ln8$) is $0$. The derivative of $-2\ln x$ using the formula $\frac{d}{dx}(\ln x)=\frac{1}{x}$ is $-2\times\frac{1}{x}$.

Answer:

$-\frac{2}{x}$