Page:Calculus Made Easy.pdf/31

 of which is $$dx$$, is similar to the original triangle; and it is obvious that the value of the ratio $$\frac{dy}{dx}$$ is the same as that of the ratio $$\frac{y}{x}$$. As the angle is $$30^\circ$$ it will be seen that here

$\frac{dy}{dx}=\frac{1}{1.73}$.

(2) Let $$x$$ represent, in Fig. 5, the horizontal distance, from a wall, of the bottom end of a ladder,



$$AB$$, of fixed length; and let $$y$$ be the height it reaches up the wall. Now $$y$$ clearly depends on $$x$$. It is easy to see that, if we pull the bottom end $$A$$ a bit further from the wall, the top end $$B$$ will come down a little lower. Let us state this in scientific language. If we increase $$x$$ to $$x+dx$$, then $$y$$ will become $$y-dy$$; that is, when $$x$$ receives a positive