# Calculus Carols

### Riemann Sums

(sung to the tune of Jingle Bells)

Riemann Sums, Riemann Sums
Counting Areas
Of rectangles whose widths get small
We need to count them all
Riemann Sums, Riemann Sums
Counting Areas
Of rectangles whose widths get small
We need to count them all.

We learn to integrate
It’s really lots of fun.
It’s easier to find
Than those old Riemann Sums
We learn to sub a u
When things get sort of hard
But most of all we tabulate
When we get sick of parts.
[repeat the refrain]

### Derivatives, Derivatives

(sung to the tune of O Christmas Tree)

Derivatives, derivatives
They help us find the rate of change.
Derivatives, derivatives
They’re not that hard, they’re in our range.

The product rule is so much fun
It’s one prime two plus two prime one
Derivatives, derivatives
They help us find the rate of change.

### Calculus Class

(sung to the tune of Silent Night)

Calculus class, calculus class
Teacher’s cruel
Hate the Chain Rule
Find the prime of f of g
It’s supposed to fill us with glee
Times dx of the outside
By dx of the inside.