Trig, ln(x) and e^x Quiz

 $y=\sin\left(e^{7x}\right)$  

Find the derivative

•  $y'=\cos\left(e^{7x}\right)\left(7\right)$  

•  $y'=7x\cos\left(e^{7x}\right)$ 

•  $y'=\sin\left(e^{7x}\right)e^{7x}$  
  

•  $y'=7\cos\left(e^{7x}\right)\left(e^{7x}\right)$  
  

•  $y'=\frac{7e^{7x}}{\cos\left(e^{7x}\right)}$  

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

• increasing
• decreasing
• concave up
• concave down

What is the average rate of change of  $y=3x^2+4x-2$   on the interval  $\left[-2,1\right]$  

• 0

• 1

• 2

• 3

At which x-value is f continuous but not differentiable?

• a
• b
• c
• d

Find $\frac{dy}{dx}$  if 

 $y=\ln\left(\sec x\right)$  

•  $\frac{dy}{dx}=\tan x\sec x$  
  

•  $\frac{dy}{dx}=\frac{1}{\tan x\sec x}$  

•  $\frac{dy}{dx}=\frac{1}{\tan x}$  
  

•  $\frac{dy}{dx}=\tan x$  
  

• A
• B
• C
• D

• A
• B
• C
• D

Find $\frac{dy}{dx}$  if  $y=\frac{\sin\left(3x\right)}{e^{2x}}$  

•  $\frac{e^{2x}\left(\cos\left(3x\right)\left(3\right)\right)-\sin\left(3x\right)e^{2x}\left(2\right)}{\left(e^{2x}\right)^2}$ 

•  $\frac{e^{2x}\cos\left(3x\right)-\sin\left(3x\right)e^{2x}}{\left(e^{2x}\right)^2}$  

•  $e^{2x}\left(\cos\left(3x\right)\left(3\right)\right)-\sin\left(3x\right)\left(e^{2x}\right)\left(2\right)$  

•  $\frac{e^{2x}\sin\left(3x\right)\left(3\right)-\sin\left(3x\right)\left(e^{2x}\right)}{\left(e^{2x}\right)^2}$  
  

Find the instantaneous rate of change of the function $y=3e^{4x}$  at x=1.

•  $7e^4$  

•  $3e^{16}$  

•  $12e^4$  
  

•  $3e^4$  
  

•  $12e$  

• A
• B
• C
• D