Page:Calculus Made Easy.pdf/36

 In ordinary algebra which you learned at school, you were always hunting after some unknown quantity which you called $$x$$ or $$y$$; or sometimes there were two unknown quantities to be hunted for simultaneously. You have now to learn to go hunting in a new way; the fox being now neither $$x$$ nor $$y$$. Instead of this you have to hunt for this curious cub called $$\frac{dy}{dx}$$. The process of finding the value of $$\frac{dy}{dx}$$ is called “differentiating.” But, remember, what is wanted is the value of this ratio when both $$dy$$ and $$dx$$ are themselves indefinitely small. The true value of the differential coefficient is that to which it approximates in the limiting case when each of them is considered as infinitesimally minute.

Let us now learn how to go in quest of $$\frac{dy}{dx}$$.