Stop This Calculus Trick Mistake Fast

Added: 2026-05-25

[00:00:03]Today we're using a fast implicit differentiation shortcut. No expansion, no wasted time, just speed and clarity.

[00:00:13]Here is the equation. X squared plus Y squared equals 25. Some students expand or rearrange, but that's slow. We skip that and differentiate immediately.

[00:00:27]Visually, this is a circle of radius five. The point we care about is X equals three, Y equals four. We will find a slope right there. Differentiate both sides. The derivative of X squared is 2X. The derivative of Y squared is 2Y * dy/dx.

[00:00:50]The derivative of 25 is zero. Now solve for dy/dx.

[00:00:57]Now plug in X equals three and Y equals four. This gives dy/dx equals -3/4.

[00:01:07]That's the slope at the point three, four.

[00:01:11]Final answer, -3/4.

[00:01:14]Fast, clean, and exactly what graders want.

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