How to Use Differentials to Estimate the Percentage Change in $r$, if $x$ increases by 6%. Let $r=6x^{-1/6}, x>0$

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I am trying to determine how to use differentials to estimate the percentage change in $r$, if $x$ increases by 6%. Let $r=6x^{-1/6}, x>0$.

So far, I have done the following steps:

1) Determine the relative change in $x$, which is $0.06$.

2) Find the differential of the equation. So, $dr = -x^{-7/6}*(dx)$

3) Divide both sides by $r$, which gives $(x^{1/6}(dx))/(-6x^{7/6})$ or $(dx)/(-6x)$

4) $(dx)/x = 0.06$, so, multiply $(-1/6)$ with $0.06$ to get $-0.01$.

5) The percentage change in r is $-1%$%

A few questions, however:

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