Question

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

y = ln x/x+1

Answer 1

`(dy)/(dx)=(1)/(x(x+1))`

Explanation:

We are given that a function

`y=ln(x)/(x+1)`

We have to find the derivative of the function

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

By using property

`ln(m)/(n)=ln m-ln n`

Differentiate w.r.t x

`(dy)/(dx)=(1)/(x)-(1)/(x+1)`

By using formula

`(d(ln x))/(dx)=(1)/(x)`

`(dy)/(dx)=(x+1-x)/(x(x+1))`

`(dy)/(dx)=(1)/(x(x+1))`

Hence, the derivative of function

`(dy)/(dx)=(1)/(x(x+1))`