Calculus 1 Review

Question 1

d/dx (x^n) = ?

Answer 1

nx^(n - 1)

Question 2

d(sin(x)) = ?

Answer 2

cos(x) • dx

Question 3

d(cos(x)) = ?

Answer 3

-sin(x) • dx

Question 4

d(tan(x))= ?

Answer 4

sec^2(x) • dx

Question 5

d(cot(x)) = ?

Answer 5

-csc^2(x) • dx

Question 6

d(sec(x)) = ?

Answer 6

sec(x) • tan(x) • dx

Question 7

d(csc(x)) = ?

Answer 7

-csc(x) • cot(x) • dx

Question 8

d(e^x) = ?

Answer 8

e^x • dx

Question 9

d(ln(x)) = ?

Answer 9

dx/x

Question 10

d(a^u) = ?

Answer 10

a^u • ln(a) • du

Question 11

d(arcsin(x)) = ?

Answer 11

dx/√(a^2 - x^2)

Question 12

d(arccos(x)) = ?

Answer 12

-dx/√(a^2 - x^2)

Question 13

d(arctan(x)) = ?

Answer 13

dx/(a^2 + x^2)

Question 14

d(arccot(x)) = ?

Answer 14

-dx/(a^2 + x^2)

Question 15

d(arcsec(x)) = ?

Answer 15

dx/(x√[(x^2) - a^2])

Question 16

d(arccsc(x)) = ?

Answer 16

-dx/(x√[(x^2) - a^2])

Question 17

{a • dx = ?

Answer 17

ax + c

Question 18

{x^n • dx = ?

Answer 18

1/(n + 1) • x^(n+1) + c

Question 19

{sin(x) • dx = ?

Answer 19

-cos(x) + c

Question 20

{cos(x) • dx = ?

Answer 20

sin(x) + c

Question 21

{tan(u) • du = ?

Answer 21

-ln|cos(u)| + c

Question 22

{cot(u) • du = ?

Answer 22

ln|sin(u)| + c

Question 23

{sec^2(x) • dx = ?

Answer 23

tan(x) + c

Question 24

{csc^2(x) • dx = ?

Answer 24

-cot(x) + c

Question 25

{sec(x) • tan(x) • dx = ?

Answer 25

sec(x) + c

Question 26

{csc(x) • cot(x) • dx = ?

Answer 26

-csc(x) + c

Question 27

{a^u • du = ?

Answer 27

(a^u)/(ln(a)) + c

Question 28

{csc(x) • dx = ?

Answer 28

ln|csc(x) - cot(x)| + c

Question 29

{sec(x) • dx = ?

Answer 29

ln|sec(x) + tan(x)| + c

Question 30

{du/(a^2 + u^2) = ?

Answer 30

(1/a) • arctan(u/a) + c

Question 31

{du/u√(u^2 - a^2) = ?

Answer 31

(1/a) • arcsec(u/a) + c

Question 32

{e^x • dx = ?

Answer 32

e^x • (1/dx) + c

Question 33

{du = ?

Answer 33

u + c

Question 34

{du/u = ?

Answer 34

ln|u| + c

Question 35

cos[(π/2) - x] = ?

Answer 35

sin(x)

Question 36

sin[(π/2) - x] = ?

Answer 36

cos(x)