Justifying the basic derivative rules

The basic derivative rules tell us how to find the derivatives of constant functions, functions multiplied by constants, and of sums/differences of functions.


Constant rule	$\frac{d}{d x} k = 0$ ‍
Constant multiple rule	$\frac{d}{d x} [k \cdot f (x)] = k \cdot \frac{d}{d x} f (x)$ ‍
Sum rule	$\frac{d}{d x} [f (x) + g (x)] = \frac{d}{d x} f (x) + \frac{d}{d x} g (x)$ ‍
Difference rule	$\frac{d}{d x} [f (x) - g (x)] = \frac{d}{d x} f (x) - \frac{d}{d x} g (x)$ ‍

The AP Calculus course doesn't require knowing the proofs of these rules, but we believe that as long as a proof is accessible, there's always something to learn from it. In general, it's always good to require some kind of proof or justification for the theorems you learn.

Let's first see why the constant rule is true.

Khan Academy video wrapper

See video transcript

Now let's prove the constant multiple and sum/difference rules.

Khan Academy video wrapper

See video transcript

Want to join the conversation?

Нэвтэрье

Sort by:

No posts yet.

Хан Академийн англи хуудас дээр ямар хэлэлцүүлэг өрнөж байгааг үзэхийг хүсвэл энд дарна уу.