Find the differential coefficients of

(7) ${\displaystyle y={\dfrac {2x+3}{3x+2}}}$.	(8) ${\displaystyle y={\dfrac {1+x+2x^{2}+3x^{3}}{1+x+2x^{2}}}}$.
(9) ${\displaystyle y={\dfrac {ax+b}{cx+d}}}$.	(10) ${\displaystyle y={\dfrac {x^{n}+a}{x^{-n}+b}}}$.

(11) The temperature ${\displaystyle t}$ of the filament of an incandescent electric lamp is connected to the current passing through the lamp by the relation

Find an expression giving the variation of the current corresponding to a variation of temperature.

(12) The following formulae have been proposed to express the relation between the electric resistance ${\displaystyle R}$ of a wire at the temperature ${\displaystyle t^{\circ }}$ C., and the resistance ${\displaystyle R_{0}}$ of that same wire at ${\displaystyle 0^{\circ }}$ Centigrade, ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ being constants.

Find the rate of variation of the resistance with regard to temperature as given by each of these formulae.

(13) The electromotive-force ${\displaystyle E}$ of a certain type of standard cell has been found to vary with the temperature t according to the relation

Find the change of electromotive-force per degree, at ${\displaystyle 15^{\circ }}$, ${\displaystyle 20^{\circ }}$ and ${\displaystyle 25^{\circ }}$.