Hi JC R.,
Assuming you wrote a single fraction as such, f(x) = (-x-3)/(x-2), this is an example of the quotient rule, which can be derived using the chain rule. Rewriting the function may be helpful:
f(x) = (-x-3) * (x-2)-1
Now you can clearly see that there are two terms being multiplied by each other, so let's apply the chain rule:
if f(x) = a(x)*b(x), then f'(x) = a'(x)*b(x) + a(x)*b'(x)
I will assume you are familiar with the power rule.
If a(x) = (-x-3) and b(x) = (x-2)-1, then we have
f'(x) = -1*(x-2)-1 + (-x-3)* -1*(x-2)-2
f'(x) = -1/(x-2) + (x+3)/(x-2)2
We can simplify by multiplying the first term by (x-2)/(x-2) and combining fractions:
f'(x) = -(x-2) + (x+3) / (x-2)2
f'(x) = 5 / (x-2)2
Now go ahead and try the next two derivatives, and let me or another tutor know if you have any other questions!
