Page 28 - Calc for the Clueless

So dy/dx = 20/115 = 4/23. We do as little work as possible. Mathematicians are very lazy by nature.

Notations

We know the notations for the first derivative. Suppose we want to take more derivatives...

Example 17—

2
2
Let us take three derivatives implicitly of X - y = 9. (Something nice usually happens in the even derivatives,
in this case the second.)

Quotient rule:

Multiply every term top and bottom
by y.

2
2
2
2
From original equation x - y = 9; therefore y - x = -9.

(Nice simplification— easy to take next
derivative).