WEBVTT

1
00:00:00.000 --> 00:00:03.158
Here is the problem: derivative of tan(x).

2
00:00:03.608 --> 00:00:06.766
Find the derivative of tan(x) with respect to x.

3
00:00:07.566 --> 00:00:11.037
d by d x[tan x] equals sec squared x.

4
00:00:11.487 --> 00:00:13.112
Combine and simplify.

5
00:00:13.912 --> 00:00:17.929
So the answer is f prime of x equals sec(x) squared.

6
00:00:18.379 --> 00:00:31.208
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
00:00:32.008 --> 00:00:38.695
Cross-checked numerically against an independent symbolic differentiator at 8 sample points, which checks out.