Differentiate First, Substitute Last

You'll learnto run a related rates problem all the way to a signed number in the one order that works, and to recognize the answer of exactly zero that a frozen variable always produces.

A 13-foot ladder slides down a wall. How fast is the top falling when the foot is 12 feet out? The whole answer hangs on the order of two steps. Eleven short steps; press Next for each one.

11 STEPS · 6 QUICK CHECKS · DIFFERENTIATE FIRST, SUBSTITUTE LAST · A FROZEN VARIABLE ANSWERS ZERO · EVERY MOVER BRINGS A RATE FACTOR · v2

x² + y² = 169 ⇒ 2x(dx/dt) + 2y(dy/dt) = 0 ⇒ dy/dt = −(x/y)(dx/dt)

Before you start

What you're looking at

A 13-foot ladder against a wall. Its foot slides out at a steady 2 feet per second, and its top slides down. The 13 never changes; everything else does.

The question

How fast is the top sliding down when the foot is 12 feet out?

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