Question Number 4219 by Yozzii last updated on 02/Jan/16
Answered by prakash jain last updated on 02/Jan/16
$${f}\:'\left(\theta\right)=\underset{\delta\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left(\theta+\delta\theta\right)−{f}\left(\theta\right)}{\delta\theta} \\ $$$$\mathrm{If}\:\mathrm{limit}\:\mathrm{exits} \\ $$$$\Rightarrow\underset{\delta\theta\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\left(\theta+\delta\theta\right)={f}\left(\theta\right)+\underset{\delta\theta\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\:'\left(\theta\right)\delta\theta \\ $$