1.
Find $\frac{dy}{dx}$ where, $y = ln(\frac{-1}{(x-1)})$
a. $\frac{1}{(x-1)}$
b. $\frac{-1}{(x-1)}$
c. $\frac{1}{(x-1)^2}$
d. $\frac{-1}{(x-1)^2}$
e. none
2. Find an equation for the tangent line to the graph of $f(x) = 2\sqrt{x}$ at $x = 4$
a. $y - 2 = \frac{1}{2}(x - 2)$
b. $y - 2 = \frac{1}{4}(x - 4)$
c. $y - 4 = \frac{1}{2}(x - 4)$
d. $y - 4 = \frac{1}{4}(x - 4)$
e. none
3. Implicitly, find $\frac{dy}{dx}|(0,0)$ where $y + cos y = x$
a. $\frac{-1}{2}$
b. $\frac{1}{2}$
c. $-1$
d. $1$
e. none
4. If $f(x) = e^{2x+1}$, then $f'(\frac{-1}{2}) = $
a. 0
b. 1
c. 2
d. -1
e. none
5. If $f(x) = x^3 + ln(x)$ then $f''(1) = $
a. 5
b. 7
c. 4
d. 6
e. none
6. If $f(x) = \frac{-(x-1)}{x+1}$ then $f'(x) = $
a. $\frac{1}{(x+1)^2}$
b. $\frac{-1}{(x+1)^2}$
c. $\frac{2}{(x+1)^2}$
d. $\frac{-2}{(x+1)^2}$
e. none
7. If $f(x) = ln(e^x)$ then $f'(x) = $
a. $e^x$
b. $ln(e^x)$
c. 1
d. $\frac{1}{e^x}$
e. none
