# Uncertainty and percentage uncertainty formulas

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