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 $f\left(x\right)=2x-5x^6$  

•  $2-30x^5$  

•  $x^2-\frac{5}{7}x^7$  
  

•  $-30x^5$  

•  $-150x^4$  
  

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

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4

Tags

CCSS.HSA.APR.A.1

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2
• 3(x²+2)/(x²+2)²
• (-3x²+4x +6)/(x²+2)²
• (-3x²+10)/(x²+2)²

Tags

CCSS.HSA.APR.D.7

Find the slope of      y= 3x² - 5 using the point x=2

• 10
• 11
• 12
• 13

Tags

CCSS.8.EE.B.5

If  $y=\frac{2x+3}{3x+2}$  , then  $\frac{\text{d}y}{\text{d}x}=$  

•  $\frac{12x+13}{\left(3x+2\right)^2}$  

•  $\frac{12x-13}{\left(3x+2\right)^2}$  

•  $\frac{5}{\left(3x+2\right)^2}$  

•  $\frac{-5}{\left(3x+2\right)^2}$  

If  $y=\left(x^3+1\right)^2$  , then  $\frac{\text{d}y}{\text{d}x}=$  

•  $\left(3x^2\right)^2$  

•  $2\left(x^3+1\right)$  

•  $2\left(3x^2+1\right)$  

•  $6x^2\left(x^3+1\right)$  

 $y=2\sqrt{x}-\frac{1}{2\sqrt{x}}$  , then  $\frac{\text{d}y}{\text{d}x}=$  

•  $x+\frac{1}{x\sqrt{x}}$  

•  $x^{-\frac{1}{2}}+x^{-\frac{3}{2}}$  

•  $\frac{4x-1}{4x\sqrt{x}}$  

•  $\frac{1}{\sqrt{x}}+\frac{1}{4x\sqrt{x}}$  

What is the derivative of cot(x)?

• sec²(x)
• -sec²(x)
• csc²(x)
• -csc²(x)

What is the derivative of csc(x)?

• csc(x)cot(x)
• -csc(x)cot(x)
• -csc²(x) 
• -cot²(x)