Flashcards in Derivatives and antiderivatives to know Deck (37)

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1

## what is the derivative of sinx?

### cosx

2

## what is the derivative of cosx

### -sinx

3

## what is the derivative of tanx

### sec²x

4

## what is the derivative of cscx

### -cscx * cotx

5

## what is the derivative of secx

### secx * tanx

6

## what is the derivative of cotx

### -csc²x

7

## what is the derivative of sin⁻¹ x

### 1 / (root of 1-x²)

8

## what is the derivative of cos⁻¹x

### - 1 / (root of 1-x²)

9

## what is the derivative of tan⁻¹x

### 1 / (1 + x²)

10

## what is the derivative of cot⁻¹x

### - 1 / (1 + x²)

11

## what is the derivative of sec⁻¹x

### 1/ ( abs. value of x times root (x²-1))

12

## what is the derivative of csc⁻¹x

### - 1/ ( abs. value of x times root (x²-1))

13

## sinx = y and sin⁻¹ ____ = ____

### y , x

14

## what is the derivative of a^x

### a^x * ln(a)

15

## what is the derivative of e^x

### e^x

16

## what is the derivative of ln(x)

### 1/x

17

## what is the derivative of log (a)^x

### 1/ (x* ln(a))

18

## what is the anti derivative of "integral" of x^n dx

### ((x^n +1)/(n+1)) +c

19

## what is the anti derivative of "integral" of e^x dx

### e^x +c

20

## what is the anti derivative of "integral" of sinx dx

### -cosx +c

21

## what is the anti derivative of "integral" of 1/(1+x^2) dx

### tan-1 x +c

22

## what is the anti derivative of "integral" of 1/ (root 1-x^2) dx

### sin-1x +c

23

## what is the anti derivative of "integral" of 1/ (abs value of x * root x^2-1) dx

### sec-1x +c

24

## what is the anti derivative of "integral" of sec^2x dx

### tanx + c

25

## what is the anti derivative of "integral" of secx tanx dx

### secx + c

26

## what is the anti derivative of "integral" of -cscx cotx dx

### cscx + c

27

## what is the anti derivative of "integral" of -csc^2x dx

### cotx + c

28

## what is the anti derivative of "integral" of k dx

### Kx + c

29

## what is the anti derivative of "integral" of 1/x dx

### ln "abs value" of x + c

30