Derivatives

What is the derivative of f(x) = 2x³ - 4x + 5?

• f'(x) = 6x² - 4x

• f'(x) = 2/3x² - 4x

• f'(x) = 3x² - 4

• f'(x) = 6x² - 4

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.IF.A.2

Which function has the derivative of g'(x) = 4x³ + 2x - 1

• g(x) = 2x⁴ + 2x² - 1

• g(x) = x⁴ + x² - x

• g(x) = 2x³ + x³ - 2x

• g(x) = x⁵ + x² - x

Tags

CCSS.HSA.APR.A.1

Choose the best rule to derive the function.

• Product rule

• Quotient rule

• Power rule

• Chain rule

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

At which point(s) will the slopes of the tangent line are zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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

•  $\frac{3}{2x}$  
  

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

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

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

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

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)