
Differentiate both sides, treating
as a function of
. Let's take it one term at a time.
Power, product and chain rules:



Product and chain rules:




Product and chain rules:




The derivative of 0 is, of course, 0. So we have, upon differentiating everything,

Isolate the derivative, and solve for it:


(See comment below; all the 6s should be 2s)
We can simplify this a bit by multiplying the numerator and denominator by
to get rid of that fraction in the denominator.

If the letters are considered distinct, then the number of permutations is

.
If we count either C as the same character, then we would be double-counting - to correct this, we would simply divided by the number of ways we can choose C from the available characters, or

.
It would be 57 suvs and 38 sedans sold to be a rational of 3:2
1.50n - 50 = p
Explanation: 1.50n = profits from selling cupcakes. Subtract from cost to make cupcakes (50) to find profit.
The answers should be:
A) 6n-4
B) -4n+25