If $z = x/y$, with $y \not = 0$. show that $\delta_z = \delta_x + \delta_y$.
I know that by multiplication rule, let $t = \frac{1}{y}$ we have $\delta_z = \delta_x + \delta_t$. But I really don't know how to show $\delta_t = \delta_y$, hope some one can help me
For these problems with relative errors, I think that logarithmic differentiation makes things a bit clearer.
$$z=\frac x y \implies \log(z)=\log(x)-\log(y)\implies \frac {dz}z=\frac {dx}x-\frac {dy}y\implies \frac {\Delta z}z=\frac {\Delta x}x-\frac {\Delta y}y$$ Since the errors accumulate, then $$\left|\frac {\Delta z}z\large \right|=\left|\frac {\Delta x}x\right|+\left|\frac {\Delta y}y\right|$$