WEBVTT

1
00:00:00.000 --> 00:00:03.529
Here is the problem: derivative of 1/x.

2
00:00:03.979 --> 00:00:07.741
Find the derivative of 1 / x with respect to x.

3
00:00:08.541 --> 00:00:15.495
Quotient rule: (u/v) prime equals (u prime v minus uv prime )/v squared.

4
00:00:15.945 --> 00:00:17.547
Combine and simplify.

5
00:00:18.347 --> 00:00:22.538
So the answer is f prime of x equals -(1 / x squared).

6
00:00:22.988 --> 00:00:35.829
The derivative is built from the outside in: sums split into terms, constants factor out, products and quotients use their rules, and every composite function multiplies by the derivative of its inside (chain rule).

7
00:00:36.629 --> 00:00:43.154
Cross-checked numerically against an independent symbolic differentiator at 8 sample points, which checks out.