The derivative of xˣ — the wrong way!
Breaking the rules is what it’s all about
I was wallowing in bed this morning, enjoying a YouTube math video. One of my favourite channels belongs to Steve Chow (aka blackpenredpen). He has a presentation in which he evaluates the derivative of xˣ. He warns us (at 4:06) against using the power rule.
I enjoy your stuff immensely, Steve. But them’s fightin’ words!
Therefore, Dear Subscribers, I present to you the derivative of xˣ — using the power rule:
The hardest part of all this was keeping the colour coding straight.[Edit: As has been pointed out to me, one of the x’s is coloured wrong.]
It’s easy to hear “undefined” and think “undefinable.” (Are you listening, square root of negative one?)
Here’s my challenge for all of you. What happens when you try to find the anti-derivative of x⁻¹ — using the reverse power rule. Can you find a way to make it work?
Send me your results at adam @ mathadam.ca. I’ll share them in a future article.
YouTube math channels for you to consider:
- blackpenredpen — Steve Chow presents challenging problems at various levels.
- Numberphile — Brady Haran interviews mathematicians about their areas of expertise.
- Mathologer — Burkard Polster makes difficult mathematics accessible. But still makes you work at it.
- 3Blue1Brown — Grant Sanderson’s remarkable visualizations of various mathematical topics.
- MathTerminds — My fledgling math channel.
Update
My solution to the challenge is here. No peeking until you’ve tried it.
