Derivative Review

Find the derivative of
 $f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$  

•  $-2x^2-x+9$  
  

•  $-2x^3-x^2+9x$  
  

•  $-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$  
  

•  $-2x^4-x^3+9x^2$  
  

Find the second derivative of the function $f\left(x\right)=2x-5x^6$  

•  $2-30x^5$  

•  $x^2-\frac{5}{7}x^7$  
  

•  $-30x^5$  

•  $-150x^4$  
  

Which of the following is the derivative of  $y=\left(3x^4-7\right)\left(5x^2+1\right)$  

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

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

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

•  $\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$  
  

Find the derivative of
 $f\left(x\right)=x^4\sin\left(x\right)$  

•  $x^4\cos\left(x\right)-4x^3\sin\left(x\right)$  
  

•  $x^4\cos\left(x\right)+4x^3\sin\left(x\right)$  
  

•  $4x^3\cos\left(x\right)$  

•  $-4x^3\cos\left(x\right)$  
  

Find the derivative of 
 $f\left(x\right)=xe^x$  

•  $f'\left(x\right)=e^x$  

•  $f'\left(x\right)=2xe^x$  

•  $f'\left(x\right)=e^x-xe^x$  
  

•  $f'\left(x\right)=e^x+xe^x$  
  

 $\frac{d}{dx}\left[\sin\left(x^3-2x\right)\right]=$  

•  $\left(3x^2-2\right)\cos\left(x^3-2x\right)$  
  

•  $-\left(3x^2-2\right)\cos\left(x^3-2x\right)$  

•  $\cos\left(3x^2-2\right)$  

•  $\sin\left(3x^2-2\right)$  

Find the derivative of
 $g\left(x\right)=\frac{3x-2}{x^2+2}$  

•  $\frac{3}{2x}$  
  

•  $\frac{3\left(x^2+2\right)}{\left(x^2+2\right)^2}$  

•  $\frac{-3x^2+4x+6}{\left(x^2+2\right)^2}$  
  

•  $\frac{9x^2-4x+6}{\left(x^2+2\right)^2}$  
  

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

• secx tanx
• sec²x
• cscx cotx
• -cscx cotx

• -cscx cotx
• cscx cotx
• -csc²x
• csc²x