Using differentials to estimate a maximum error

Four positive numbers lesser than 50 each are rounded to the first decimal and then multiplied between themselves. Use differentials to estimate the maximum possible error of the product.

My attempt : Let $\displaystyle x$, $\displaystyle y$ and $\displaystyle z$ be the 3 numbers.

We have $\displaystyle (x+\Delta x)(y+\Delta y)(z+\Delta z)=0.1(zx+zy+xy)+0.01(z+x+y)+0.001$.

Note that I considered $\displaystyle \Delta x = \Delta y = \Delta z =0.1$.

However I don't see how I can use differentials. I don't see any way to involve them. So I didn't solve the problem...

Do you have any idea?