Derivative of Composite Function/Examples/Logarithm of x over x + 1

Example of Derivative of Composite Function

 * $\map {\dfrac \d {\d x} } {\ln \dfrac x {x + 1} } = \dfrac 1 {x \paren {x + 1} }$

Proof
Let $u = \dfrac x {x + 1}$.

Let $y = \ln u$.

Thus we have:
 * $y = \ln \dfrac x {x + 1}$

and so: