Product rule Memes

The rare moment when YouTube's auto-generated quiz actually got the math right! Taking the derivative of (3e 4 * x) requires the product rule: (first function × derivative of second) + (second function × derivative of first). Since the derivative of x is 1 and the derivative of 3e 4 is 0 (it's a constant), we get 3e 4 × 1 + x × 0 = 3e 4 . The fourth option is correct, but what's truly miraculous is that an AI quiz generator didn't mess up basic calculus. Next thing you know, YouTube will be solving Fermat's Last Theorem in the comments section!

Oh, the forbidden mathematical fantasy! What we're looking at here is the calculus equivalent of asking if you can split your restaurant bill by just paying for what you ordered. The equation falsely claims that the integral of a product equals the product of the integrals—a mathematical sin so egregious it makes calculus professors wake up in cold sweats. For those who slept through Calc I, this is like wishing that (2×3) = (2+3). Pure mathematical heresy! Yet every semester, some hopeful soul writes this on an exam, as if begging the universe to suspend its laws just this once. Dream on, sweet summer child.

The left book represents actual calculus—thick, comprehensive, and full of complex integration rules. The right book? That's "calculus if" the integral of a product equaled the product of integrals. The equation shown (∫f(x)*g(x)dx = ∫f(x)dx * ∫g(x)dx) is hilariously wrong and would collapse most of mathematics if true. It's the mathematical equivalent of saying "what if gravity was optional?" The thin book perfectly captures how much simpler—and utterly broken—calculus would be if this mathematical crime were allowed. Every calculus student's forbidden dream!

Every math student's fantasy right here! The left shows calculus as the massive, soul-crushing tome it truly is. The right shows the beautiful dream world where the integral of a product equals the product of the integrals. If only mathematics worked that way, we'd all have graduated with our sanity intact. For the uninitiated, that property is mathematically incorrect and would make calculus infinitely easier. It's the equivalent of wishing multiplication distributed over division. Mathematicians have spent centuries developing integration techniques precisely because this shortcut doesn't work. The thinner book represents the collective tears of generations of calculus students who've desperately wished for this mathematical miracle.