So I am curious how does one derive the following relations for uncertainties:

Let $p=cxy$ or $p = c\dfrac{x}{y}$ and $r =z^n$ where $c=constant$

  • $\dfrac{\Delta p}{p} = \dfrac{\Delta x}{x}+\dfrac{\Delta y}{y}$
  • $\dfrac{\Delta r}{r} = n \dfrac{\Delta z}{z}$

Attept to solution

so I know that let's say if $x=2.0\pm0.1$ then $x_{w}=2.1, x_{b}=2.0$ and $\Delta x=x_w-x_b$ and $\dfrac{\Delta x}{x}=\dfrac{x_w-x_b}{x_b}$

Now if

$\dfrac{\Delta p}{p}= \dfrac{p_w-p_b}{p_b}= \dfrac{cx_wy_w-cx_by_b}{cx_by_b} = \dfrac{x_wy_w}{x_by_b}-1\equiv \dfrac{x_w-x_b}{x_b}+\dfrac{y_w-y_b}{y_b}$

how are the two equivalent? I can't get the right side equal the left or other way around


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