Derivatives Review

Find dy/dx for
y = 8x⁷

• dy/dx = x⁸
• dy/dx = 7x⁶
• dy/dx = 12x⁶
• dy/dx = 56x⁶

Find dy/dx for 
y = (x² + 1)³

• dy/dx = 3(x² + 1)²
• dy/dx = 3(2x)²
• dy/dx = 6x(x² + 1)²
• dy/dx = 2x(x² + 1)²

Tags

CCSS.HSF-IF.C.8B

d/dx (sin²x) = ?

• 2sin x
• 2(sin x)(cos x)
• 2cos x
• 2x(cos x)

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
 $f\left(x\right)=x^4\sin\left(x\right)$  

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

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

•  $4x^3\cos\left(x\right)$  

•  $-4x^3\cos\left(x\right)$  
  

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

•  $f'\left(x\right)=e^x$  

•  $f'\left(x\right)=2xe^x$  

•  $f'\left(x\right)=e^x-xe^x$  
  

•  $f'\left(x\right)=e^x+xe^x$  
  

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

•  $\frac{3}{2x}$  
  

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

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

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

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

d/dx (sin²x) = ?

• 2sin x
• 2(sin x)(cos x)
• 2cos x
• 2x(cos x)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

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

Tags

CCSS.HSF.TF.C.8