# Examples of Derivatives of Logarithmic Functions

Example: Differentiate ${\log _{10}}\left( {\frac{{x + 1}}{x}} \right)$ with respect to $x$.

Consider the function

Differentiating both sides with respect to $x$, we have

Example: Find $\frac{{dy}}{{dx}}$, if the given function is $y = {x^{\cos y}}$

We have the given function

Taking $\ln$ on both sides of the given function, we have

Differentiating both sides with respect to $x$, we have