> For the complete documentation index, see [llms.txt](https://yingshaoxo.gitbook.io/university-notes/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://yingshaoxo.gitbook.io/university-notes/high-level-math/derivative-and-differential/goes-deeper.md).

# Goes deeper

Something like $$\frac{a}{b}$$, split by $$-$$, we call $$a$$ `Molecular`, $$b$$ `Denominator`.

$$
\begin{align\*}
f(x) &= x^2
\ \\
&\Downarrow \text{Take derivative of the previous formula}
\ \\
f^\prime(x) &= 2x    &(x^2)^\prime &= 2x
\ \\
&\Downarrow \text{Take derivative of the previous formula}
\ \\
f^{\prime \prime}(x) &= 2    &(2x)^\prime &= 2
\end{align\*}
$$

We say $$f^\prime(x)$$ is the first derivative of $$f(x)$$, $$f^{\prime \prime}(x)$$ is the second derivative of $$f(x)$$. You can keep doing this by changing the number before `derivative`, for example, 3 derivative of ...