Mathematics

This problem asks you to think about what derivatives mean in terms of units, not just how to compute them. When you take a derivative, you're finding the rate of change of one quantity with respect to another—and the units of that rate are always (units of numerator) per (units of denominator). For $\frac{dT}{dr}$, you're asking "how much does temperature change per unit change in radius?" For $\frac{dT}{dt}$, you're asking "how much does temperature change per unit change in time?" The key is to let the definition of the derivative guide your unit labels.

This problem asks you to think about what derivatives mean in terms of units, not just how to compute them. When you take a derivative, you're finding the rate of change of one quantity with respect to another—and the units of that rate are always (units of numerator) per (units of denominator). For $\frac{dT}{dr}$, you're asking "how much does temperature change per unit change in radius?" For $\frac{dT}{dt}$, you're asking "how much does temperature change per unit change in time?" The key is to let the definition of the derivative guide your unit labels.