Rashi tells us in Devarim 11:30 by the words הֲלֹא־הֵ֜מָּה בְּעֵ֣בֶר הַיַּרְדֵּ֗ן אַֽחֲרֵי֙ דֶּ֚רֶךְ מְב֣וֹא הַשֶּׁ֔מֶשׁ that
"אַחֲרֵי" נָקוּד בְּפַשְׁטָא, וְ"דֶרֶךְ" נָקוּד בְּמַשְׁפֵּל, וְהוּא דָּגֵשׁ, וְאִם הָיָה "אַחֲרֵי דֶרֶךְ" דִּבּוּר אֶחָד, הָיָה נָקוּד "אַחֲרֵי" בִּמְשָׁרֵת, בְּשׁוֹפָר הָפוּךְ, וְ"דֶרֶךְ" בְּפַשְׁטָא וְרָפָה
There Rashi teaches us that if a word ends in a yud, the first letter of the next word does not have a dagesh. The only reason that there is a dagesh in the דּ in דֶּרֶךְ is because the words אַֽחֲרֵי and דֶּרֶךְ are not connected.
However, in Shemot 15:11, the pasuk tells us that מִ֥י כָּמֹ֖כָה נֶאְדָּ֣ר בַּקֹּ֑דֶשׁ, who is like you, majestic in holiness. Despite that fact that the word מִי ends in a yud, the כָּ in כָּמֹ֖כָה still has a dagesh in it. You could say that this is like אַֽחֲרֵי and דֶּרֶךְ in Devarim, however, the words מִי and כָּמֹכָה are related and would not make sense without each other. So, why is there a dagesh in the כּ in מִ֥י כָּמֹ֖כָה נֶאְדָּ֣ר בַּקֹּ֑דֶשׁ?
