Answer:
D
Step-by-step explanation:
did it on edge
Answer:
The inner function is 
and the outer function is 
.
The derivative of the function is 
.
Step-by-step explanation:
A composite function can be written as 
, where 
and 
are basic functions.
For the function 
.
The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.
Here, we have 
inside parentheses. So is the inner function and the outer function is .
The chain rule says:
![\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%3Df%27%28g%28x%29%29g%27%28x%29)
It tells us how to differentiate composite functions.
The function is the composition, , of
outside function:
inside function:
The derivative of this is computed as
The derivative of the function is .
In an installment loan, a lender loans a borrower a principal amount P, on which the borrower will pay a yearly interest rate of i (as a fraction, e.g. a rate of 6% would correspond to i=0.06) for n years. The borrower pays a fixed amount M to the lender q times per year. At the end of the n years, the last payment by the borrower pays off the loan.
After k payments, the amount A still owed is
<span>A = P(1+[i/q])k - Mq([1+(i/q)]k-1)/i,
= (P-Mq/i)(1+[i/q])k + Mq/i.
</span>The amount of the fixed payment is determined by<span>M = Pi/[q(1-[1+(i/q)]-nq)].
</span>The amount of principal that can be paid off in n years is<span>P = M(1-[1+(i/q)]-nq)q/i.
</span>The number of years needed to pay off the loan isn = -log(1-[Pi/(Mq)])/(q log[1+(i/q)]).
The total amount paid by the borrower is Mnq, and the total amount of interest paid is<span>I = Mnq - P.</span>
Those two added together are equal to
14 and
