A Story Told in Derivatives

Thanks for sharing this \href{https://twitter.com/oliviawalch}{Olivia}, and also Austin and Swarna for the great examples! \href{http://www-personal.umich.edu/~ojwalch/swarna-austin/index.html}{original source}

{\bf Math Myths}

created by Austin Rife, Swarna Shil


When looking at a power function, we can imagine the exponent as Mt. Olympus where the gods live. The variable is the mortal humans, but we have a magic mortal-making potion called the power rule. We can use this potion to throw one of the gods down to live with mortals, which multiplies the power of mortals but leaves Mt. Olympus with one less god.


$$ \frac{d}{dx} x^5 = 5x^4 $$
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$a^x$ was a narcissist. He always liked to lean ($\ln$) down to see his reflection in the pool
($a$).

$$f(x) = a^x$$
$$f ’(x) = a^x \ln(a)$$

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Apollo and Artemis are a famous pair for their moody behaviors in Mt. Olympus and the mortal world, but no one knows the true mystery behind these two. Apollo ($\sin(x)$) is actually Artemis ($\cos(x)$) when he uses the $\frac{d}{dx}$ potion. When he uses the $\frac{d}{dx}$ potion again as Artemis, he becomes the evil Apollo $–\sin(x)$. And when evil Apollo takes it once more, he becomes evil Artemis. Evil Artemis transforms into good Apollo with another boost of the $\frac{d}{dx}$ potion. Thus, this moody behavior of the divine “twins” continues in an endless cycle.


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