# Math Help - Rates of Change: Sensitivity

1. ## Rates of Change: Sensitivity

Let R be the reaction of the body to some stimulus of strength s (measured in the appropriate units). The sensitivity S is defined to be the rate of change of the reaction with repect to s. Suppose that, for the particular R and s, the following experimental formula has been used:

R=（20+28s^0.9）/(1+9s^0.9)

The sensitivity S at $s=1$ equals _____ (units of )/(units of )

how can I find the unit of the sensitivity

I get s=64.08 but I don't know how to defined the unit

2. Originally Posted by shannon1111
Let R be the reaction of the body to some stimulus of strength s (measured in the appropriate units). The sensitivity S is defined to be the rate of change of the reaction with repect to s. Suppose that, for the particular R and s, the following experimental formula has been used:

R=（20+28s^0.9）/(1+9s^0.9)

$S=\dfrac{dR}{ds}$

I've got $\dfrac{dR}{ds}=\dfrac{-136.8}{s^{0.1} \cdot \left(9s^{0.9}+1\right)^2}$

The sensitivity S at $s=1$ equals _____ (units of )/(units of )
With my result I get S(1) = -1.368

how can I find the unit of the sensitivity

I get s=64.08 how? but I don't know how to defined the unit

3. ohhhhhhh,I got the calculation part wrong....
Thanks