calculus - Number of real roots of $f ' ( x )$

Let $$f(x)=(x-a)(x-b)^3(x-c)^5(x-d)^7 $$
where $a,b,c,d$
are real numbers with
$a < b < c < d$
. Thus $ f
(
x
)$ has $16$ real roots counting multiplicities and among them $4$ are

distinct from each other. Consider
$f
'
(
x
)$, i.e. the derivative of
$f
(
x
)$. Find the following:
$(i)$ the number of real roots of

$f
'
(
x
)$, counting multiplicities,
$(ii)$ the number of
distinct
real roots of
$f
'
(

x
)$.

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This is a polynomial of degree $16$ hence the derivative will be of degree $15$ and hence it will have $15$ roots. But are they real ?
How to find distinct real roots ? Rolle's theorem tells only about existence of root.