Calc: Derivatives L2 Review

Which rules should you use to find the derivative of $y=\ π\tan x\ -\ln x$  ?

• Power Rule

• Product Rule

• Special Derivatives
  

• None of the above
  

Which rule should you first use to find the derivative of $y=\ 3x^2e^x$  ?

• Power Rule

• Product Rule

• Special Derivatives
  

• None of the above
  

Which rule should you use to find the derivative of $y=\ 2x^4+6x^3-x\ +\ 5$   ?

• Power Rule

• Product Rule

• Special Derivatives
  

• None of the above
  

 $\$  

Find the derivative of  $f\left(x\right)=8e^x\ -\ 10\ln x$ 

•  $f'\left(x\right)=8e^x\ -\ \frac{10}{x}$  

•  $f'\left(x\right)=e^{8x}\ -\ 10x$  

•  $f'\left(x\right)=e^x\ -\ \frac{1}{x}$  

•  $f'\left(x\right)=8e^x\ +\ \frac{10}{x}$  

Tags

CCSS.HSF-IF.C.8B

Find the derivative of  $y\ =\ 6\cot x-2\sec x$  

•  $y'=-6\csc x\cot x-2\tan x$  

•  $y'=6\sec^2x+2\csc x\cot x$  

•  $y'=-6\csc^2x-2\sec x\tan x$  

•  $y'=6\csc^2x+2\sec x\tan x$  
  

Given  $f\left(x\right)=4\sin x-2e^x$  , find  $f'\left(0\right)$  

Tags

CCSS.HSF.IF.A.2

Which is NOT an acceptable way to write the product rule?

• y'(x)=f'(x)g(x)+f(x)g'(x)

• y'(x)=f(x)g'(x)+f'(x)g(x)

• y'(x)=g(x)f'(x)+g'(x)f(x)

• y'(x)=f'(x)f(x)+g(x)g'(x)

 $\$  Set up the derivative of y = $(3x^4-7)(5x^2+1)$  

•  $\left(12x^3\right)\left(10x\right)$  
  

•  $(12x^3)(5x^2+1)+(3x^4-7)(10x)$  

•  $(12x^3)(5x^2+1)-(3x^4-7)(10x)$  

•  $(12x^3-7)(5x^2+1)+(3x^4-7)(10x+1)$  

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²

• 18x² - 16x

• 15x² - 6x

• 6x - 4

 $\$  Find and fully simplify the derivative of  $5x\left(\ln x\right)$  

•  $5x\left(\ln x\right)+5$  

•  $5\ln\left(x\right)+5$  

•  $5x\ln\left(x\right)+5x\ln\left(x\right)$  

•  $5xe^x+5\ln\left(x\right)$