Question

find $\frac{dy}{dx}$. $y = 8log_2 x$. $\frac{dy}{dx}=square$ (simplify your answer.)

Explanation:

Step1: Use change - of - base formula

First, use the change - of - base formula $\log_a x=\frac{\ln x}{\ln a}$. So, $y = 8\log_2x=8\frac{\ln x}{\ln 2}$.

Step2: Differentiate

The derivative of a constant times a function is the constant times the derivative of the function. The derivative of $\ln x$ with respect to $x$ is $\frac{1}{x}$. So, $\frac{dy}{dx}=\frac{8}{\ln 2}\times\frac{d}{dx}(\ln x)$.

Step3: Get the result

Since $\frac{d}{dx}(\ln x)=\frac{1}{x}$, then $\frac{dy}{dx}=\frac{8}{x\ln 2}$.

Answer:

$\frac{8}{x\ln 2}$