One Factor Per Layer

You'll learnwhy the derivative of sin(3x) is cos(3x) times 3, and how to spot the factor most students drop.

y = sin(3x) is two machines in series: triple x, then take the sine. Nudge x, and how fast does y move at the far end? Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · RATES MULTIPLY · ONE FACTOR PER LAYER · THE DROPPED FACTOR · v2

one factor per layer · dy/dx = f′(g(x)) · g′(x)

Before you start

What you're looking at

Two machines in a row. x goes into the first, its output u goes into the second, and y comes out the far end.

The question

If the inside runs three times as fast as x, how fast does y move?

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