00:01
So in this question, they say the table below gives values of differential functions, f and g, and i'm going to use the table to answer the question below.
00:09
If h of x is equal to x minus f of x over g of x, then h prime of negative 1 is equal to which of the following.
00:18
So let's see.
00:19
If i want h prime of negative 1, i need h prime of f.
00:24
And that's going to require the quotient rule.
00:27
The quotient rule says i start with my denominator, g of x, times.
00:33
The derivative of the numerator.
00:36
The derivative of the numerator is 1 minus f prime of x.
00:42
Minus the numerator, my numerator is x minus f of x times the derivative of the denominator g prime of x all over my denominator being squared.
00:58
G of x being squared.
01:01
And so now i want each prime of negative 1.
01:08
So let's see.
01:09
I've got g of negative 1.
01:12
G of negative 1, that is 1, times the quantity of 1 minus f prime of negative 1.
01:22
F prime of negative 1, that is 5 minus the quantity of x, negative 1, minus f of x.
01:34
So this is going to be f of negative 1, f of negative 1, f of negative 1 is 3, times g prime of negative 1...