Force derived from Yukawa potential

This is with regards to problem 3.19 from Goldstein’s Classical Mechanics,

A particle moves in a force field described by the Yukowa potential $$ V(r) = -frac{k}{r} e^{-frac{r}{a}},
$$ where $k$ and $a$ are positive.

where I bolded the assumptions as this is the only information I can imagine helps me resolve this.

A solution due to Professor Laura Reina at Florida State Uni, as well as a solution due to Slader.com

both use the following expression for the force felt by a particle in the given Yukawa potential:

$$
F(r) = -frac{k}{r^2} e^{-frac{r}{a}}
$$

I am struggling to wrap my head around this. This is clearly not the result of

$$ -frac{partial V(r)}{partial r} $$

which evaluates to

$$
-frac{k}{r^2} e^{-frac{r}{a}} – frac{k}{ar} e^{-frac{r}{a}}
$$

Can anyone help me understand why the second term $-frac{k}{ar} e^{-frac{r}{a}}$ can be excluded here? I tried plotting some various example of this, varying k and a which are allowed to be any positive numbers, but I’ve no insight.

There was a question regarding this same topic which was not answered Deriving potential from central force