Patterns

Decreasing power with derivatives

As fun as it is to work out derivatives using deltas like $\Delta x$, and seeing what happens when we make them smaller and smaller, we can often do it without doing all that work.

Let’s see if we can decipher a pattern in the derivatives we’ve worked out so far:

$$s = t^2 \rightarrow \frac {\partial s}{\partial t} = 2t$$

$$s = t^2 + 2t \rightarrow \frac {\partial s}{\partial t} = 2t + 2$$

$$s = t^3 \rightarrow \frac {\partial s}{\partial t} = 3t^2$$