I am trying to do sensitivity analysis on a given function by calculating the 1st-order (partial) derivatives. In a simple case let's say the function is $y=ax^2$.

Then the 1st-order derivative is: $\frac{dy}{dx}=2ax$ (1)

The relative sensitivity indices is calculated as $\frac{dy}{y}/\frac{dx}{x}=2$. (2)

My question is how to interpret this relative sensitivity indices? I have read that it can be interpreted as: 2% changes in $y$ if 1% changes in $x$. But if we think of increasing $x$ 1% to have $x'=1.01x$ and $y'=a(1.01x)^2$, so it is obviously $(y'-y)/y\neq2(x'-x)/x$ as we see in formula (2). Can someone give more insights on the meaning of the relative sensitivity indices and in what case it is more informative than the raw first derivate $dy$?



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