HW 2G Exponential & Log Derivatives

What is the derivative of e^x?

• xe^x-1
• x^e
• e^x
• e^x-1

Find the derivative f(x) = xe^x

*Hint: you will need product rule

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

What is the derivative of ln(x)?

• xln(x)
• 1/x
• e^x
• ln(x+1)

Tags

CCSS.HSF.BF.B.5

If $y=10^x$  then  $\frac{\text{d}y}{\text{d}x}=$  

•  $x10^{x-1}$  

•  $10^x$  

•  $10^x\cdot\ \ln\left(10\right)$  

•  $9^x$  

If $y=\log_2\left(x\right)$  then  $\frac{\text{d}y}{\text{d}x}=$  

•  $\frac{1}{\log_2\left(1\right)x}$  

•  $\frac{2}{\log_2\left(2\right)x}$  

•  $\frac{1}{\ln\left(2\right)x}$  

•  $\frac{2}{\ln\left(1\right)x}$  

If $y=x^2e^x$  then  $\frac{\text{d}y}{\text{d}x}=$  

*Hint: you will need product rule

•  $2x^2\cdot e^x$  

•  $2x\cdot e^x$  

•  $2x\cdot e^x+x^2\cdot e^x$  

•  $\left(x^2+1\right)e^x$  

What is the derivative of  $a^u$  ?

•  $\ln\left(a^u\right)$  
  

•  $\frac{1}{a^u}$  

•  $a^u\cdot\ln\left(a\right)$  

•  $\frac{u}{\ln\left(a\right)}$  
  

What is the derivative of  $\log_b\left(x\right)$  ?

•  $b^x$  

•  $\frac{1}{\ln\left(b\right)}$  

•  $\frac{1}{x\cdot\ln\left(b\right)}$  

•  $\ln\left(b^x\right)$  

Evaluate the limit:

 $\lim_{x\rightarrow1}\left(\frac{3\ln\left(x\right)-3\ln\left(1\right)}{x-1}\right)$  

• 3

• 1/3

• ln(3)

• 3ln(1)

Evaluate the limit:

 $\lim_{h\rightarrow0}\left(\frac{3\left(x+h\right)^2+5^{\left(x+h\right)}-3x^2-5^x}{h}\right)$  

•  $6x+5^x\cdot\ln\left(5\right)$  
  

•  $3+5\ln\left(x\right)$  
  

•  $3+5^x\ln\left(5\right)$  
  

•  $6x+5\cdot\ln\left(x\right)$