In problems #1-5, find the Derivative of each expression. Use correct notation for each Derivative! Algebraic simplification of each Derivative result is NOT required. In problems #6-7, solve then evaluate as stated.

1) f(x) = e^x + 9x^-3 + 2e^1.5

2) g(t) = 4t^2.5 + ln t + e^-t

3) y = ln x^3.5 - ln 36 + lne^X

4) y = 2.4w³ + ln w - 6 e^-W

5) f(x) = log₅ X + 8^X (Note: Logarithmic and exponential terms do not have a natural base 'e' in this problem.)

6) If $3500 is deposited into an account with 5.279% nominal annual interest compounded continuously:

a) Find total accumulation in the account after 12 years. Show formula. Solve to the nearest penny. Show all work!

6b) Find the total amount of interest accumulated after 12 years. Show formula. Solve to the nearest penny.

6c) Since 5.279% is the nominal rate of interest in this problem, what is the effective rate of interest? Show the formula you are using. Solve to six decimal places.

7) How long would it take a $10,000 deposit to grow to $22,500 in an account with 6.249% nominal annual interest compounded continuously? Solve for time (in years) to four decimal places. Show all your work!