Contrapositive of the statement:
'If a function $$f$$ is differentiable at $$a$$, then it is also continuous at $$a$$', is

We begin with the original statement, which is an implication:
    $$P : \text{The function } f \text{ is differentiable at } a$$
    $$Q : \text{The function } f \text{ is continuous at } a$$
Stated in words, the implication is “If $$P$$, then $$Q$$” or symbolically $$P \Rightarrow Q$$.

To find its contrapositive, we recall the logical rule:
    Formula for contrapositive: For any implication $$P \Rightarrow Q$$, the contrapositive is $$\lnot Q \Rightarrow \lnot P$$.
That is, we first negate the conclusion $$Q$$, then make it the new hypothesis; simultaneously we negate the original hypothesis $$P$$ and make it the new conclusion.

Applying this rule step by step:

1. Negate the conclusion $$Q$$.
    The negation of “$$f$$ is continuous at $$a$$” is “$$f$$ is not continuous at $$a$$”.
    So $$\lnot Q : \text{The function } f \text{ is not continuous at } a$$.

2. Negate the hypothesis $$P$$.
    The negation of “$$f$$ is differentiable at $$a$$” is “$$f$$ is not differentiable at $$a$$”.
    So $$\lnot P : \text{The function } f \text{ is not differentiable at } a$$.

3. Form the new implication $$\lnot Q \Rightarrow \lnot P$$.
    In sentence form this reads: “If the function $$f$$ is not continuous at $$a$$, then $$f$$ is not differentiable at $$a$$.”

We now compare this derived contrapositive with the given options:

Option A: “If $$f$$ is continuous at $$a$$, then it is not differentiable at $$a$$.” (This is $$Q \Rightarrow \lnot P$$, not the contrapositive.)

Option B: “If $$f$$ is not continuous at $$a$$, then it is not differentiable at $$a$$.” (This matches $$\lnot Q \Rightarrow \lnot P$$ exactly.)

Option C: “If $$f$$ is not continuous at $$a$$, then it is differentiable at $$a$$.” (This is $$\lnot Q \Rightarrow P$$, the inverse of Option A, still incorrect.)

Option D: “If $$f$$ is continuous at $$a$$, then it is differentiable at $$a$$.” (This is simply the converse of the original statement.)

Only Option B reproduces the contrapositive. Hence, the correct answer is Option B.