You are given the following function.
f(t) = t + √t
Find the derivative of the function using the definition of derivative.

Question

You are given the following function.
f(t) = t + √t
 Find the derivative of the function using the definition of derivative.

anonymous · Answer

$$\begin{align*}f'(t)&=\lim_{h\to0}\frac{f(t+h)-f(t)}{h}\
&=\lim_{h\to0}\frac{(t+h+\sqrt{t+h})-(t+\sqrt t)}{h}\
&=\lim_{h\to0}\frac{h+\sqrt{t+h}-\sqrt t}{h}\
&=\lim_{h\to0}\frac{h}{h}+\lim_{h\to0}\frac{\sqrt{t+h}-\sqrt t}{h}\
&=\lim_{h\to0}1+\lim_{h\to0}\frac{\sqrt{t+h}-\sqrt t}{h}\
&=1+\lim_{h\to0}\frac{\sqrt{t+h}-\sqrt t}{h}
\end{align*}$$
What do you think you can do about those square roots?

anonymous · Answer

Try multiplying by the conjugate