+0

# help finding derivative

0
222
1

I was confused on how to find the derivative of this function:

y = log2(x/(x-1)

If anyone could help me, please and thank you!!!

Mar 25, 2019

### 1+0 Answers

#1
+6192
+2

$$y=\log_2\left(\dfrac{x}{x-1}\right) = \dfrac{1}{\ln(2)}\ln\left(\dfrac{x}{x-1}\right)\\ \dfrac{dy}{dx} = \dfrac{1}{\ln(2)}\cdot \dfrac{1}{\dfrac{x}{x-1}}\cdot \left(\dfrac{(x-1)-x}{(x-1)^2}\right)= \\ -\dfrac{1}{\ln(2)}\cdot \dfrac{x-1}{x}\cdot \dfrac{1}{(x-1)^2} = \\ -\dfrac{1}{\ln(2)}\dfrac{1}{x(x-1)} =\\ \dfrac{1}{\ln(2)}\dfrac{1}{x(1-x)}$$

.
Mar 25, 2019