Pregunta: diferenciar: g(theta)=e^(theta)*(tan(theta)-(theta))

Differentiate using the Product Rule which states that $\frac{\mathrm{d}}{\mathrm{d}\theta }\left[\mathrm{f}\left(\theta \right)\mathrm{g}\left(\theta \right)\right]$ is $\mathrm{f}\left(\theta \right)\frac{\mathrm{d}}{\mathrm{d}\theta }\left[\mathrm{g}\left(\theta \right)\right]+\mathrm{g}\left(\theta \right)\frac{\mathrm{d}}{\mathrm{d}\theta }\left[\mathrm{f}\left(\theta \right)\right]$ where $\mathrm{f}\left(\theta \right)={\mathrm{e}}^{\theta }$ and $\mathrm{g}\left(\theta \right)=\tan \left(\theta \right)-\theta$ .

${\mathrm{e}}^{\theta }\frac{\mathrm{d}}{\mathrm{d}\theta }[\tan \left(\theta \right)-\theta ]+(\tan \left(\theta \right)-\theta )\frac{\mathrm{d}}{\mathrm{d}\theta }\left[{\mathrm{e}}^{\theta }\right]$