WEBVTT

1
00:00:00.000 --> 00:00:04.180
Here is the problem: d by d x 3 to the power x.

2
00:00:04.630 --> 00:00:08.995
Find the derivative of 3 to the power x with respect to x.

3
00:00:09.795 --> 00:00:17.318
Exponential rule: d by d x[aᵘ] equals aᵘ times ln(a) times u prime.

4
00:00:17.768 --> 00:00:19.289
Combine and simplify.

5
00:00:20.089 --> 00:00:25.882
So the answer is f prime of x equals 3 to the power x times ln(3).

6
00:00:26.332 --> 00:00:39.289
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
00:00:40.089 --> 00:00:46.846
Cross-checked numerically against an independent symbolic differentiator at 8 sample points, which checks out.