Solution assignment 26 Chain rule

Differentiate:

$y=\ln(\displaystyle\frac{x^2-2x}{x})$

We can easily simplify the function:

$\displaystyle\frac{x^2-2x}{x}=x-2$

By doing so, we avoid to use the quotient rule. The function that has to be differentiated becomes:

$y=\ln(x-2)$

Applying the informal chain rule yields (the 'quote' means: the derivative of):

$y'=\displaystyle\frac{1}{x-2}\cdot(x-2)'=\displaystyle\frac{1}{x-2}$

Note that this derivative is not valid for $x=0$ .