Is this process for finding derivative of R(t)= A*sqrt(t-T)/t correct? Work is already done. I just need someone to look over.

Question

jade085 · Answer

This is the work

jade085 · Answer

@Preetha ?

mww · Answer

you shouldn't have squared the 2. in the second line, only the sqrt(t-T) is squared

mww · Answer

However you still arrived at the correct answer, just be careful of using parentheses...

jade085 · Answer

@mww thanks

kainui · Answer

Just a tip, I like something called implicit differentiation since it makes my life easier and maybe it will for you too. I basically just rearrange it so there are no fractions are square roots with algebra from:

$$R = \frac{A\sqrt{t-T}}{t}$$
into
$$R^2 t^2 = A^2 (t-T)$$
Then I take the derivative,

$$2RR't^2 + R^22t = A^2$$
That whole left part I didn't even write on my paper cause I know $R'=0$ so everything multiplying it is 0.

$$R^22t=A^2$$
At this point, I see I need $R^2$ so I square the original function and plug it in, here's what $R^2$ looks like:
$$R^2 = \frac{A^2 (t-T)}{t^2}$$ 
Now pluggin in:

$$\frac{A^2 (t-T)}{t^2}2t=A^2$$$$2(t-T)=t$$$$t=2T$$

I find this much less painful cause I hate fractions haha.