Question

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

Answer 1

Yikes...
\[\Large f(t) = t + \sqrt t\]

\[\Large f'(t) = \lim_{h\rightarrow 0}\frac{f(t+h)-f(t)}{h}\]
This will not be pretty lol

Answer 2

I'm sure you've gotten at least that^ far.
What you have got now? ^_^

Answer 3

\[1 + \lim_{h \rightarrow 0} \frac{ \sqrt{t + h} - \sqrt{t}}{ h } \]
what's next?

Answer 4

Hmmnn...

Answer 5

argh... this is why nobody does it this way XD...
hang on

Answer 6

Okay, try multiplying with this:
\[\Large \frac{\sqrt{t+h}+\sqrt t}{\sqrt {t+h}+ \sqrt t}\]

Answer 7

@swedishlad bet you already got there before me xD

Answer 8

\[1 +\lim_{h \rightarrow 0}\frac{ h }{ h(\sqrt{t+h}+\sqrt{t}) }\]

Answer 9

You can cancel out the h now
\[\Large 1 +\lim_{h \rightarrow 0}\frac{ \cancel h }{ \cancel h(\sqrt{t+h}+\sqrt{t}) }\]

Answer 10

And you'd be done lol

Answer 11

\[\frac{ 1 }{ 2\sqrt{t}} + 1\]

Answer 12

boom, thanks man

Answer 13

No problem ^_^