# Thread: [SOLVED] Find the rate of change of F with respect to V

1. ## [SOLVED] Find the rate of change of F with respect to V

The frequency of F of a siren heard by a stationary observer is given by;
F= 132,400/[331 (+-) V], where (+-) V represents the velocity of the accelerating fire truck. Find the rate of change of F with respect to V when,
a.) the fire truck is approaching at a velocity of 30m/s (use -V) and when
b.) the fire truck is moving away at a velocity of 30m/s (use + V)

Well what i did was first differentiate 132,400/[331 (+-) V], substituting the numbers with variables. Let a= 132,400 and b= 331; my answer was
-a/ [b (+-) V)^2]. From that I worked out number a where i used -V and for number b i used +V. My answers of that I don't know what to do with them... I don't know it is just that, if they are correct that is, or i need to do more. For a.) i got -1.46 and the other -1.02..

2. Looks right to me. No need to substitute other variables as you did, though. The derivative is $\frac {-132400}{(331+V)^2}$, as per the quotient rule, and I would state it that way. The +/- is also somewhat not relevant. Just consider the denominator to be (331 + V) and use an appropriate positive or negative V when you substitute in the values for V.

However, nitpicking aside, those results are correct as far as I can tell.
Grep.

P.S. It would all be more readable if you used LaTex to format your math. It's not too complicated to figure out, and there's a forum where you can learn how to use it. Just a small suggestion.

P.P.S. Oh yeah, noticed a missing parenthesis in your derivative.