Intro to Calculus - Chapter 3 Test Multiple Choice Section

What is the derivative of xⁿ

• (n+1)xⁿ⁺¹
• (n-1)x^n-1
• nxⁿ⁺¹
• nx^n-1

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Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.A.1

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Tags

CCSS.HSA.REI.B.4

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Given $f\left(x\right)=17$  , what is the derivative of  $f\left(x\right)$  ?

•  $f'\left(x\right)=17x$  

•  $f'\left(x\right)=17$  

•  $f'\left(x\right)=0$  

•  $f'\left(x\right)=17x^2$  

If  $f\left(x\right)=e^x,\ then\ f'\left(x\right)=?$  

•  $\ln\left(x\right)$  
  

•  $e^x$  
  

•  $-e^x$  
  

•  $\frac{1}{e^x}$  

Tags

CCSS.HSF.BF.B.5

 $If\ f\left(x\right)=\cos\left(x\right),\ then\ f'\left(x\right)=?$  

•  $\sin\left(x\right)$  
  

•  $\cos\left(x\right)$  
  

•  $-\sin\left(x\right)$  
  

•  $-\cos\left(x\right)$  
  

Tags

CCSS.HSF.TF.A.2

 $If\ y=\log_3x,\ then\ \frac{dy}{dx}=?$  

•  $\frac{1}{x\ln3}$  

•  $\frac{x}{\ln x}$  

•  $\frac{e^3}{x}$  

•  $\frac{\ln3}{x}$  

Tags

CCSS.HSF-IF.C.8B

Find the first derivative of  $y=\left(x^3+19\right)^7$  

•  $\frac{\text{d}y}{\text{d}x}=21x^2\left(x^3+19\right)^6$  

•  $\frac{\text{d}y}{\text{d}x}=21x^3\left(x^3+19\right)^6$  

•  $\frac{\text{d}y}{\text{d}x}=3x^2\left(x^3+19\right)^6$  

•  $\frac{\text{d}y}{\text{d}x}=7x^2\left(x^3+19\right)^6$  

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)