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,

Fig. 5.

$AB$, 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