how do you find the derivative of f(t)=t-sqrt(t) by the definition of a derivative.

Question

anonymous · Answer

\begin{eqnarray*} \frac{f(t + h) - f(t)}{h} &=& \frac{t + h - \sqrt{t + h} - (t - \sqrt{t})}{h}\ &=& \frac{h + \sqrt{t} - \sqrt{t + h}}{h} \ &=& 1 - \frac{\sqrt{t + h} - \sqrt{t}}{h} \ &=& 1 - \frac{t + h - t}{h(\sqrt{t + h} + \sqrt{t})} \&=& 1 - \frac{1}{\sqrt{t + h} + \sqrt{t}} \&\xrightarrow{h\ 	o\ 0}& 1 - \frac{1}{\sqrt{t + 0} + \sqrt{t}} \ &=& 1- \frac{1}{2\sqrt{t}}.\end{eqnarray*}

anonymous · Answer

wow! thanks I feel terrible. I made a stupid mistake and got caught up