Question

find the derivative of y with respect to x.

( y = 6 ln left( \frac { 16 } { x }
ight) )

( \frac { d y } { d x } = )

Explanation:

Step1: Use logarithm property

Use $\ln(\frac{a}{b})=\ln a-\ln b$. So $y = 6(\ln16-\ln x)=6\ln16 - 6\ln x$.

Step2: Differentiate term - by - term

The derivative of a constant ($6\ln16$) is $0$. The derivative of $-6\ln x$ using the formula $\frac{d}{dx}(\ln x)=\frac{1}{x}$ and the constant - multiple rule $\frac{d}{dx}(cf(x))=c\frac{d}{dx}(f(x))$ (where $c = - 6$ and $f(x)=\ln x$). So $\frac{dy}{dx}=0-6\times\frac{1}{x}$.

Answer:

$-\frac{6}{x}$