Derivative Rules Flashcards

1

\frac{d}{dx}x^2=

2x
x
2x^2
2x^3

2

\frac{d}{dx}\ln x

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

3

\frac{d}{dx}\cot x

\sec^2x
-\sec^2x
\csc^2x
-\csc^2x

4

\frac{d}{dx}x=

0
2x
x
1

5

\frac{d}{dx}f\cdot s

f'\cdot s'
f'\cdot s+s'\cdot f
s'\cdot f+f'\cdot s
f\cdot f'+s\cdot s'

6

\frac{d}{dx}\csc x

\csc x\cot x
-\csc x\cot x
\sec x\tan x
-\sec x\tan x

7

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

\frac{-1}{\left|x\right|\sqrt{x^2-1}}
\frac{-1}{\left|x\right|\sqrt{1-x^2}}
\frac{1}{\left|x\right|\sqrt{1-x^2}}
\frac{1}{\left|x\right|\sqrt{x^2-1}}

8

\frac{d}{dx}a^x=(where a is a constant)

xa^{\left(x-1\right)}
a^x
x^a
\ln a\cdot a^x

9

\frac{d}{dx}\cos x

\sin x
-\sin x
\cos x
-\cos x

10

\frac{d}{dx}8=

8x
x2
0
8

11

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

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

12

\frac{d}{dx}\sin x

-\sin x
\sin x
-\cos x
\cos x

13

\frac{d}{dx}3x^2=

3x^2
3x^3
6x
3x

14

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

xe^{x-1}
xe^x
e^x
e^{x-1}

15

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

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

16

\frac{d}{dx}\log_ax=

\frac{1}{x}
\ln a
\frac{1}{a}
\frac{1}{x\ln a}

17

\frac{d}{dx}\frac{t}{b}=

\frac{b'\cdot t'-b\cdot t}{b^2}
\frac{b\cdot t'-t\cdot b'}{b^2}
\frac{t'}{b'}
\frac{t\cdot b'-b\cdot t'}{b^2}

18

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

\frac{1}{\left|x\right|\sqrt{x^2-1}}
\frac{-1}{\left|x\right|\sqrt{1-x^2}}
\frac{-1}{\left|x\right|\sqrt{x^2-1}}
\frac{1}{\left|x\right|\sqrt{1-x^2}}

19

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

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

20

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

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

21

\frac{d}{dx}\tan x

\sec^2x
-\sec^2x
\csc^2x
-\csc^2x

22

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

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

23

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

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

24

\frac{d}{dx}\sec x

\csc x\cot x
-\sec x\tan x
-\csc x\cot x
\sec x\tan x

Derivative Rules

Questions 24

Derivative Rules

Questions 24