What sort of persuasive language or persuasive techniques are used in Hamlet?I'm doing an English assignment where I have to explain the ways...

This sounds like a really interesting assignment! Good
luck with it. You might want to think about the following example of persuasive language
in this play. Of course, like most Shakespeare plays, it contains lots of examples, but
Act IV scene 7 to me is the best one to focus on when Claudius meets with Laertes and
manipulates him. It is well worth revisiting this scene and examining it closely because
here we see how Claudius persuades Laertes to kill Hamlet for
him.

One of the key elements of this scene to me is when
Claudius mocks Laertes to spur him on in anger to revenge against Hamlet. Note how
Claudius says to Laertes:

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Laertes was your father dear to
you?

Or are you like the painting of a
sorrow,

A face without a
heart?

Claudius is
deliberately angering Laertes to manipulate his emotions. By questioning the sincerity
of his love he goads Laertes into a rash revenge plot - completely unlike Hamlet, of
course, for Laertes does not hesitate at all in achieving his goal of revenge. Note how
Claudius goes on to challenge Laertes following this insulting
question:

What
would you undertake,

To show yourself your father's son
indeed,

More than in
words?

The challenge is clear
- if you do love your father, show it but not in words. What are you prepared to
do?

So is hatched the final revenge plan that brings death
to both Laertes and Claudius. I have highlighted some of the examples you will want to
think about but it is well worth considering the scene as a whole to pick up more
examples of persuasive language. Good luck!