Integrals and Derivatives

Question 1

Derivative of C

Answer 1

0

Question 2

Derivative of mx + c

Answer 2

m

Question 3

derivative of x^a

Answer 3

ax^(a-1)

Question 4

derivative of ae^(kx)

Answer 4

(ak)e^(kx)

Question 5

derivative of aIn(kx)

Answer 5

a/x

Question 6

Derivative of sin x

Answer 6

cos x

Question 7

Derivative of cos x

Answer 7

-sin x

Question 8

Derivative of tan x

Answer 8

sec^2(x)

Question 9

Derivative of cot x

Answer 9

-csc^2(x)

Question 10

Derivative of sec x

Answer 10

sec(x)tan(x)

Question 11

Derivative of csc x

Answer 11

-csc(x)cot(x)

Question 12

Derivative of sin^-1(x)

Answer 12

1/sqrt(1-x^2)

Question 13

Derivative of cos^-1(x)

Answer 13

-1/sqrt(1-x^2)

Question 14

Derivative of tan^-1(x)

Answer 14

1/(1+x^2)

Question 15

Derivative of cot^-1(x)

Answer 15

-1/(1+x^2)

Question 16

Derivative of sec^-1(x)

Answer 16

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

Question 17

Derivative of csc^2(x)

Answer 17

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

Question 18

Integral of a

Answer 18

ax + c

Question 19

Integral of ax^n

Answer 19

ax^(n+1)/n+1 + C

Question 20

Integral of ax^-1

Answer 20

aIn|x| + C

Question 21

Integral of ae^kx

Answer 21

a/k e^kx + C

Question 22

Integral of sin x

Answer 22

-cos x + C

Question 23

Intergral of cos x

Answer 23

sin x + C

Question 24

Integral of tan x

Answer 24

In|sec x| + C

Question 25

Integral of cot x

Answer 25

In|sin x | + C

Question 26

Integral of sec x

Answer 26

In|tan x + sec x| + C

Question 27

Integral of a/ (bx + c)

Answer 27

a/b In|bx + c| + C

Question 28

Integral of a/(bx + c)^n

Answer 28

a(bx+c)^1-n/(b(1-n) + C