1. The problem asks how to get the expression $dl = \frac{d\ell(w)}{dw}$. 2. This expression represents the derivative of a function $\ell(w)$ with respect to the variable $w$. 3. The derivative $\frac{d\ell(w)}{dw}$ measures how the function $\ell(w)$ changes as $w$ changes. 4. To find $dl$, which is the differential change in $\ell$, we use the rule: $$dl = \frac{d\ell(w)}{dw} dw$$ This means the small change in $\ell$ is the derivative times the small change in $w$. 5. In plain terms, if you know how $\ell$ changes per unit change in $w$ (the derivative), then multiplying by a small change in $w$ gives the corresponding small change in $\ell$. 6. This is a fundamental concept in calculus called the differential, and it helps approximate changes in functions. Final answer: $$dl = \frac{d\ell(w)}{dw} dw$$