# Thread: story problem implicit differentiation

1. ## story problem implicit differentiation

please someone smart help to get me going, i dont know how to start these

"A 20 foot ladder is leaning against a building. The bottom of the ladder is sliding along the pavement directly away from the building at 1 foot per second. How fast is the top of the ladder moving down when the foot of the ladder is 5 feet away from the wall?"

i know this uses the pythagorean theorem somehow... i dont know what to do though

2. Pythagoras Theorem

$
\frac{dx}{dt}= 1
$

$x^2+y^2 = 400$

Differentiate both sides with respect to t

Hence

$
2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0
$

Put $\frac{dx}{dt} =1$

So

$
\frac{dy}{dt} = \frac{- 2x}{2y}
$

$
\frac{dy}{dt} = \frac{-x}{y}

$