Source: 
Problem diagram.
Black's response to the marked stone?
Keshi and Uchikomi, Kaoru Iwamoto 9 dan
Solution follows
(or click here to download SGF)
Correct.
Every go player must know what to do if White makes the diagonal
play after Black invades. Pushing out with Black 1 is necessary.
After White blocks with 2, Black 3 is the move to know.
After White protects the cut with 8, Black can connect out on the edge with 9. Finally, White finishes in gote with 10, but gains nice outside influence.
Dozens of variations exist depending on the surrounding stones, but the
simple themes here are common to many of those positions.
White variation.
Stopping Black from connecting out with White 8 might
look dangerous but is bad for White.
Black can make obvious moves up to 13. And if the ladder works for Black, White collapses after the obvious forcing moves starting with Black 15. The sequence is somewhat long, but simple and easy to remember.
If the ladder is good for White, Black is still OK. See the
next diagram.
Black variation.
If the ladder in the previous diagram is good for White,
Black can live easily against the edge with 15.
If White tries to kill with 16, Black has a trivial sequence
through 21. White collapses. Again, the sequence is somewhat long,
but simple and easy to remember.
A Black mistake.
Black 3 is bad timing.
After White 4, Black loses a critical liberty.
Now if Black tries to connect out with 5, White 6
captures the invading stones.
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