Derivatives and antiderivatives to know

Question 1

what is the derivative of sinx?

Answer 1

cosx

Question 2

what is the derivative of cosx

Answer 2

-sinx

Question 3

what is the derivative of tanx

Answer 3

sec²x

Question 4

what is the derivative of cscx

Answer 4

-cscx * cotx

Question 5

what is the derivative of secx

Answer 5

secx * tanx

Question 6

what is the derivative of cotx

Answer 6

-csc²x

Question 7

what is the derivative of sin⁻¹ x

Answer 7

1 / (root of 1-x²)

Question 8

what is the derivative of cos⁻¹x

Answer 8

• 1 / (root of 1-x²)

Question 9

what is the derivative of tan⁻¹x

Answer 9

1 / (1 + x²)

Question 10

what is the derivative of cot⁻¹x

Answer 10

• 1 / (1 + x²)

Question 11

what is the derivative of sec⁻¹x

Answer 11

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

Question 12

what is the derivative of csc⁻¹x

Answer 12

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

Question 13

sinx = y and sin⁻¹ ____ = ____

Answer 13

y , x

Question 14

what is the derivative of a^x

Answer 14

a^x * ln(a)

Question 15

what is the derivative of e^x

Answer 15

e^x

Question 16

what is the derivative of ln(x)

Answer 16

1/x

Question 17

what is the derivative of log (a)^x

Answer 17

1/ (x* ln(a))

Question 18

what is the anti derivative of “integral” of x^n dx

Answer 18

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

Question 19

what is the anti derivative of “integral” of e^x dx

Answer 19

e^x +c

Question 20

what is the anti derivative of “integral” of sinx dx

Answer 20

-cosx +c

Question 21

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

Answer 21

tan-1 x +c

Question 22

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

Answer 22

sin-1x +c

Question 23

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

Answer 23

sec-1x +c

Question 24

what is the anti derivative of “integral” of sec^2x dx

Answer 24

tanx + c

Question 25

what is the anti derivative of “integral” of secx tanx dx

Answer 25

secx + c

Question 26

what is the anti derivative of “integral” of -cscx cotx dx

Answer 26

cscx + c

Question 27

what is the anti derivative of “integral” of -csc^2x dx

Answer 27

cotx + c

Question 28

what is the anti derivative of “integral” of k dx

Answer 28

Kx + c

Question 29

what is the anti derivative of “integral” of 1/x dx

Answer 29

ln “abs value” of x + c

Question 30

what is the anti derivative of “integral” of cosx dx

Answer 30

sinx +c

Question 31

what is the anti derivative of “integral” of -1/ (1+x^2) dx

Answer 31

cot-1x + c

Question 32

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

Answer 32

cos -1x +c

Question 33

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

Answer 33

csc -1x + c

Question 34

what is the anti derivative of “integral” of tanx dx

Answer 34

-ln lcosxl + c

Question 35

what is the anti derivative of “integral” of cotx dx

Answer 35

ln lsinxl + c

Question 36

what is the anti derivative of “integral” of secx dx

Answer 36

ln lsec + tanxl + c

Question 37

what is the anti derivative of “integral” of cscx dx

Answer 37

ln lcscx -cotxl + c