# Calculus Problem

#### Mathmasteriw

##### Junior Member
Hi guys and girls,
Can anyone double check my work here?
I belive I am correct here.
Differentiate the funcion with respect to ‘t’ and have shown the ‘rate of change’ when t is 5

looks fine

#### Otis

##### Elite Member
$$\displaystyle \frac{dv}{dt}(5)$$ …
Hi Mathmasteriw. That's an interesting form of function notation that I've never seen before. I'm curious. Where did you see it?

#### HallsofIvy

##### Elite Member
I have seen that in many places.
$$\displaystyle \frac{dv}{dt}(5)= \frac{dv(5)}{dt}$$.
meaning the derivative of v with respect to t, evaluated at t=5
Some people would prefer the first to the second on the grounds that the second could be interpreted as the derivative of the constant v(5) which is, of course, 0.

#### Jomo

##### Elite Member
Personally I think the answer is (dv/dt)(5) = -2e^(-2.5) or -2/e^2.5. -.164 is an approximation and not the exact answer.

#### Otis

##### Elite Member
… -0.164 is an approximation and not the exact answer.
Good point, Jomo, but we don't know for sure what the given instructions may have said.

#### Otis

##### Elite Member
I have seen that [derivative notation] in many places …
Thanks, Halls. It prompted me to think of and ponder this:

$\frac{\text{dv}}{\text{dt}} \bigg\rvert_{5} = -0.164$

I've never seen that done, either, but it makes sense.

… Some people would prefer [$$\; \frac{dv}{dt}(5) \;$$] to [$$\; \frac{dv(5)}{dt} \;$$] …
Agree!

#### Jomo

##### Elite Member
How I look at it is that $$\displaystyle \dfrac{dv}{dt}$$ is a function of t. Just because the name of the function is a bit strange looking does not change its notion. $$\displaystyle \dfrac{dv}{dt}=\dfrac{dv}{dt}(t)$$ and $$\displaystyle \dfrac{dv}{dt}$$ evaluated at t= 5 is denoted as $$\displaystyle \dfrac{dv}{dt}(5)$$.

I have used this notation frequently. I have also seen $$\displaystyle \dfrac{dv}{dt}(5)$$ written as $$\displaystyle \dfrac{dv}{dt}|_{t=5}$$

#### Mathmasteriw

##### Junior Member
Hi Mathmasteriw. That's an interesting form of function notation that I've never seen before. I'm curious. Where did you see it?

I owe a lot to what I have learned to this page

#### topsquark

##### Senior Member
$$\displaystyle \dfrac{dv}{dt}|_{t=5}$$
If memory serves me I've seen this in many forms in Math texts but the above quote is the only way I've seen Physicists write it.

-Dan