Question

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Answer 1

Answer:

$\frac{dy}{dx}=\frac{1}{x(x+1)}$

Step-by-step explanation:

We are given that a function  

$y=ln\frac{x}{x+1}$

We have to find the derivative of the function  

$y=lnx-ln(x+1)$

By using property

$ln\frac{m}{n}=ln m-ln n$

Differentiate w.r.t x

$\frac{dy}{dx}=\frac{1}{x}-\frac{1}{x+1}$

By using formula

$\frac{d(ln x)}{dx}=\frac{1}{x}$

$\frac{dy}{dx}=\frac{x+1-x}{x(x+1)}$

$\frac{dy}{dx}=\frac{1}{x(x+1)}$

Hence, the derivative of function

$\frac{dy}{dx}=\frac{1}{x(x+1)}$