Upper a 18a 18? -footfoot ladder is leaning against a building. if the bottom of the ladder is sliding along the pavement directly away from the building at 22 ? feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 44 feet from the? wall?

The foot of the ladder cannot be 44 feet from the wall, that would be larger than the length of the ladder, which means the ladder has crawled a few feet :)

So we are assuming a distance of 4 feet, similarly a rate of change in x equal to 2ft/s.

check the picture.

let 

be the function of the height of the ladder with respect to x, the distance of the bottom of the ladder to the wall.

We want , the rate of change of h with respect to t.

h is a function of x and x is a function of t, so we keep this in mind as we derivate h with respect to t:



we substitute  and x=4:

ft/s