Any help on this Calculus problem?

[Mathmasteriw]

Hello Everybody,
I wonder if anybody can help me with this problem?
Is this the final answer with respect to t?
Is it correct? Where am I going wrong ?
Thank you for your time!

 

[Dr.Peterson]

Isn't this the same question as https://www.freemathhelp.com/forum/threads/help-with-function.127118/, which we helped you with before?

Your answer happens to be right, but your work is nonsense. You didn't use the chain rule, and then you made it seem like x and t are the same thing.

Look back at what you were told before, and try again.

 

[Mathmasteriw]

Yep same question!
I'm not sure how to lay the question out to present the answer.

i will try again thanks for your time

 

[pka]

$V(t)=\log(f(t))\\f(t)=2t$ so we have $\dfrac{dV}{dt}=\dfrac{f'(t)}{f(t)}=\dfrac{2}{2t}=\dfrac{1}{t}$

 

[Steven G]

Based on your work you are not using the correct formula. What follows next is what you should do to update all your other formulas.

$$If\ y = A\log_eU,\ then\ y' = \dfrac {A}{U}\dfrac{dU}{dt}$$. So in all your derivative formulas you should replace all x's (or t's or q's,...) with U and then multiply by dU/dx (or dU/dt or dU/dq,...)

In your case U = 2t. So $$\dfrac{dU}{dt}\ =\ 2$$

 

[Mathmasteriw]

Thanks for your help guys! Will try that one again shortly! ?