# Equation of sensitivity

1. Dec 2, 2011

1. Function, F is dependent on variable a; and the sensitivity is

$$S = \frac{\frac{\delta{F}}{F}}{\frac{\delta{a}}{a}}$$

2. My question is what if F is a function of two variable, a and b? In that case what would be the sensitivity equation? Is it something like:

$$S = \frac{\frac{\delta{F}}{F}}{\frac{\delta{a}}{a} \frac{\delta{b}}{b}}$$

3. I am trying to formulate a problem with sensitivity equation and do not know what to do at this point. May be the equation is very simple, therefore could not find in literature. Any help, link would be appreciated.

2. Dec 2, 2011

### HallsofIvy

Staff Emeritus
What does $\delta Fp$ mean? Is that a differential or the slight change in F given a slight change in x? What would it mean if there were two variables? Perhaps you want a measure of sensitivity to change in each variable?

3. Dec 2, 2011

Thanks for your reply. Actually the definition of sensitivity states "how the variation in the output of a model can be attributed to different variations in the inputs of the model". I meant to use partial derivative symbol here therefore. Now if function F is only dependent on variable a, the answer is straightforward as given in point 1. But I want to know if function F is dependent on two variables (a,b) then how would it look like.

You can take an example like,

$$1. F = \frac{a}{1-a} 2. F = \frac{a b^2}{(1-a)(1-b)}$$

4. Dec 2, 2011