Derivatives and antiderivatives to know Flashcards Preview

AP Calculus AB > Derivatives and antiderivatives to know > Flashcards

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

what is the anti derivative of "integral" of cosx dx

sinx +c