David,

On slide 7 you show a rule.

y= 10+3x -x^3

y’= 3+3x^2

I have 2 questions

so the ‘ of a constant times X is the constant?

why does -x^3 become positive

I am sorry for not giving you the EB lesson number itr is 5

Hi Frank,

1. Yes, y’(aX) = a where a is a constant (if “with respect to X"). You might think of this as but a case of the power rule (on slide #8)

y = f(x) = (k)(x^n)
y’ = (k)(n)(x^(n-1))

because you have

y = f(x) = (k)(x^1), so
y’ = (k)(1)(x^0) = (k)(1)(1) = k

2. an error, which has been cited before (alas it is hard to edit video!), so your instincts are good here:

should be
y’ = 3 - 3*X^2

BTW, you may tire of me on this, but this “first (partial) derivative” is IMO the first building block in the whole FRM. (I’ll collect two or three dozen for the cram, but this is first, pun intended). Risk is sensitivity (rate of change) to the factor, so it may help to keep in mind this first derivative is a “sheep with many clothes”

option delta: first derivative
bond duration: function of 1st derivative
Jorion’s component/marginal VaR: 1st derivatives (change in portfolio VaR given change in component)
Ong’s risk contribution: 1st derivative

David