## Calculus, 10th Edition (Anton)

Logarithm rules state that a logarithm with base $b$ can be rewritten as $$\frac{ln(x)}{ln(b)}$$ Taking the derivative of the new expression, $\frac{ln|x|}{ln(b)}$, by separating the constant $\frac{1}{ln(b)}$ yields $$\frac{1}{x \times ln(b)}=\frac{1}{xln(b)}$$