AP Calc Derivatives and Integrals

Question 1

Derivative of ( c ) (where ( c ) is a constant)

Answer 1

0

Question 2

Derivative of ( x^n ) (power rule)

Answer 2

n x^{n-1}

Question 3

Derivative of ( sin(x) )

Answer 3

cos(x)

Question 4

Derivative of ( cos(x) )

Answer 4

-sin(x)

Question 5

Derivative of ( an(x) )

Answer 5

sec^2(x)

Question 6

Derivative of ( cot(x) )

Answer 6

-csc^2(x)

Question 7

Derivative of ( sec(x) )

Answer 7

sec(x)tan(x)

Question 8

Derivative of ( csc(x) )

Answer 8

-csc(x)cot(x)

Question 9

Derivative of ( e^x )

Answer 9

e^x

Question 10

Derivative of ( a^x ) (where ( a > 0 ))

Answer 10

a^x ln(a)

Question 11

Derivative of ( ln(x) )

Answer 11

1/x

Question 12

Derivative of ( log_a(x) )

Answer 12

1/(x ln(a))

Question 13

Derivative of ( arcsin(x) )

Answer 13

1/sqrt(1-x^2)

Question 14

Derivative of ( arccos(x) )

Answer 14

-1/sqrt(1-x^2)

Question 15

Derivative of ( arctan(x) )

Answer 15

1/(1+x^2)

Question 16

Derivative of ( arccot(x) )

Answer 16

-1/(1+x^2)

Question 17

Derivative of ( arcsec(x) )

Answer 17

1/|x|sqrt(x^2-1)

Question 18

Derivative of ( arccsc(x) )

Answer 18

-1/|x|sqrt(x^2-1)

Question 19

Integral of ( c , dx )

Answer 19

cx + C

Question 20

Integral of ( x^n , dx ) (where ( n
eq -1 ))

Answer 20

x^{n+1}/(n+1) + C

Question 21

Integral of ( sin(x) , dx )

Answer 21

-cos(x) + C

Question 22

Integral of ( cos(x) , dx )

Answer 22

sin(x) + C

Question 23

Integral of ( sec^2(x) , dx )

Answer 23

tan(x) + C

Question 24

Integral of ( csc^2(x) , dx )

Answer 24

-cot(x) + C

Question 25

Integral of ( sec(x)tan(x) , dx )

Answer 25

sec(x) + C

Question 26

Integral of ( csc(x)cot(x) , dx )

Answer 26

-csc(x) + C

Question 27

Integral of ( e^x , dx )

Answer 27

e^x + C

Question 28

Integral of ( a^x , dx ) (where ( a > 0 ))

Answer 28

a^x/ln(a) + C

Question 29

Integral of ( rac{1}{x} , dx )

Answer 29

ln|x| + C

Question 30

Integral of ( rac{1}{1+x^2} , dx )

Answer 30

arctan(x) + C

Question 31

Integral of ( rac{1}{sqrt{1-x^2}} , dx )

Answer 31

arcsin(x) + C