Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/164



EXAMPLES

Differentiate the following, using differentials:

14. $$d \left [ \frac{x \log x}{1 - x} + \log(1 - x) \right ] = \frac{\log x dx}{(1 - x)^2}$$.

15. $$d [ \arctan \log y] = \frac{dy}{y[1 + (\log y)^2]}$$.

16. $$d \left [ r \operatorname{arcvers} \frac{y}{r} - \sqrt{2ry - y^2} \right ] = \frac{y dy}{\sqrt{2ry - y^2}}$$.

17. $$d \left [ \frac{\cos \psi}{2 \sin^2 \psi} - \frac{1}{2} \log \tan \frac{\psi}{2} \right ] = -\frac{d\psi}{\sin^3 \psi}$$.