# How do you find the derivative of #ln(x/(x^2+1))#?

##### 1 Answer

Jan 22, 2017

#### Explanation:

The easiest way is to first rewrite the function using properties of logarithms. Recall that

#f(x)=ln(x/(x^2+1))#

#f(x)=ln(x)-ln(x^2+1)#

Now we have two simpler functions to differentiate. Recall that

Then:

#f'(x)=1/x-(d/dx(x^2+1))/(x^2+1)#

#f'(x)=1/x-(2x)/(x^2+1)#

These can be combined, but it's not necessary:

#f'(x)=(x^2+1-2x(x))/(x(x^2+1))#

#f'(x)=(1-x^2)/(x^3+x)#