# BC Calculus Assignment 36: Exponentials Worksheet B

• Class: 5H: BC Calculus
• Author: Peter Atlas
• Text: Calculus Finney, Demana, Waits, Kennedy

1. Use the fact that $$y = \ln {x}$$ and $$y = e^x$$ are inverses of each other to simplify the following expressions:
1. $$e^{\ln {7}}$$
2. Solution 7
3. $$e^{3 \ln {2 }}$$
4. Solution 8
5. $$e^{-2 \ln {3 }}$$
6. Solution $$\frac{1}{9}$$
7. $$e^{2 + \ln {3 }}$$
8. Solution $$3e^2$$
2. Solve the following for $$y$$.
1. $$\ln {y} = 2t + 4$$
2. Solution $$y = e^{2t + 4}$$
3. $$\ln {(1 - 2y)} = t$$
4. Solution $$y = \frac{e^t - 1}{ -2}$$
5. $$5 + \ln {y} = 2 ^{x^2 + 1}$$
6. Solution $$y = e^{2^{x^2 + 1} - 5}$$
7. $$\ln {(2^y - 1)} = x^2 - 3$$
8. Solution $$y = \frac{ \ln{ \left( e^{x^2 - 3} + 1 \right) }}{\ln{2}}$$
3. Find $$\frac{dy}{dx}$$.

1. $$y = 2e^x$$
2. Solution $$y' = 2e^x$$
3. $$y = e^{-\frac{x}{4}}$$
4. Solution $$y' = -\frac{1}{4} e^{-\frac{x}{4}}$$
5. $$y = x^2e^x - xe^x$$
6. Solution $$y' = e^x(x^2 + x - 1)$$
7. $$y = e^{x^2}$$
8. Solution $$y' = 2xe^{x^2}$$