Page:Calculus Made Easy.pdf/170

 We see that, since

We shall find that whenever we have an expression such as $$\log_\epsilon y =$$ a function of $$x$$, we always have $$\dfrac{1}{y}\, \dfrac{dy}{dx} =$$ the differential coefficient of the function of $$x$$, so that we could have written at once, from $$\log_\epsilon y = x \log_\epsilon a$$,

Let us now attempt further examples.

Examples.

(1) $$y=\epsilon^{-ax}$$. Let $$-ax=z$$; then $$y=\epsilon^z$$.

Or thus:

(2) $$y=\epsilon^{\frac{x^2}{3}}$$. Let $$\dfrac{x^2}{3}=z$$; then $$y=\epsilon^z$$.

Or thus: