I am studying error theory. I don't understand from where does $\ln$ appear at the end
Consequently, the marginal absolute error of the approximated value of the function $y^*$ is calculated by the formula $$ A_{y^*}=\sum_{i=1}^n\left|f_{x_i}^{\prime}\left(x^*\right)\right| A_{x_i} . $$ Then, using the definition of the marginal relative error of the approximate value of $y^*$ , we obtain a formula for its finding $$ \Delta_{y^*}=\frac{A_{y^*}}{\left|y^*\right|}=\sum_{i=1}^n\left|\frac{\partial\ln f\left(x^*\right)}{\partial x_i}\right| A_{x_i^*} . $$