AP AB Calculus Derivatives Quiz Flashcards

1

\frac{d}{dx}\tan x

\sec x\tan x
\tan x\sec x
\sec^2x
\sec x

2

\frac{d}{dx}\csc^{-1}x

\frac{-1}{|x|\sqrt{x^2+1}}
\frac{-1}{\sqrt{x^2+1}}
\frac{-1}{|x|\sqrt{x^2-1}}
\frac{-1}{\sqrt{x^2-1}}

3

\frac{d}{dx}\sec x

\tan^2x
\tan x
\sec x\tan x
\tan x\sec x

4

\frac{d}{dx}\log_bx

x\ln b
\frac{1}{x\ln b}
b\ln x
\frac{1}{b\ln x}

5

\frac{d}{dx}\cos x=\sin x

False
True

6

\frac{d}{dx}a^x=x\ln a

False
True

7

\frac{d}{dx}\tan^{-1}x

\frac{1}{x^2+1}
\frac{-1}{x^2-1}
-\frac{1}{x^2+1}
\frac{1}{x^2-1}

8

\frac{d}{dx}\cot^{-1}x

\frac{1}{x^2+1}
\frac{-1}{x^2+1}
\frac{1}{x^2-1}
\frac{-1}{x^2-1}

9

\frac{d}{dx}\cot x

-\csc x\cot x
-\csc^2x
-\csc x
\csc^2x

10

\frac{d}{dx}\cos^{-1}x

\frac{-1}{\sqrt{1+x^2}}
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{x^2+1}
\frac{1}{\sqrt{1-x^2}}

11

\frac{d}{dx}\csc x

-\cot^2x
-\csc x\cot x
-\cot x\csc x
\csc x\cot x

12

\frac{d}{dx}e^x=e^x

False
True

13

\frac{d}{dx}x^n=nx^n

True
False

14

\frac{d}{dx}\frac{u}{v}

\frac{uv´-u´v}{v^2}
\frac{uv´+u´v}{v^2}
\frac{u´v+uv´}{v^2}
\frac{u´v-uv´}{v^2}

15

\frac{d}{dx}\sec^{-1}x

\frac{1}{|x|\sqrt{x^2-1}}
\frac{1}{\sqrt{x^2+1}}
\frac{1}{|x|\sqrt{x^2+1}}
\frac{1}{\sqrt{x^2-1}}

16

\frac{d}{dx}\left(uv\right)

u'v-uv'
uv'+u'v
u'v+uv'
uv'-u'v

17

\frac{d}{dx}\ln x=\frac{1}{x}

False
True

18

\frac{d}{dx}f\left(g\left(x\right)\right)

f'\left(g\left(x\right)\right)g\left(x\right)
f\left(g\left(x\right)\right)g'\left(x\right)
f\left(g'\left(x\right)\right)f'\left(x\right)
f'\left(g\left(x\right)\right)g'\left(x\right)

19

\frac{d}{dx}\sin^{-1}x

\frac{1}{\sqrt{1+x^2}}
\frac{1}{x^2+1}
\frac{1}{\sqrt{1-x^2}}
\frac{-1}{\sqrt{1-x^2}}

20

Limit Definition of a Derivative: m=f'\left(x\right)=

\lim_{h\to0}\frac{f\left(x+h\right)+f\left(x\right)}{h}
\lim_{h\to0}\frac{f\left(x-h\right)+f\left(x\right)}{h}
\lim_{h\to0}\frac{f\left(x-h\right)-f\left(x\right)}{h}
\lim_{h\to0}\frac{f\left(x+h\right)-f\left(x\right)}{h}

AP AB Calculus Derivatives Quiz

Questions 20

AP AB Calculus Derivatives Quiz

Questions 20