Derivatives & Integrals

Question 0

Derivative of sinx

Answer 0

Cosx

Question 1

Derivative of cotx

Answer 1

-csc^2x

Question 2

Derivative of Cosx

Answer 2

-sinx

Question 3

Derivative of tanx

Answer 3

Sec^2x

Question 4

Derivative of secx

Answer 4

Secxtanx

Question 5

Derivative of cscx

Answer 5

-cscxcotx

Question 6

Derivative of lnu

Answer 6

1/u du/dx

Question 7

Derivative of e^u

Answer 7

e^u du/dx

Question 8

Derivative of sin inverse

Answer 8

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

One over the square root of 1-x^2

Question 9

Derivative of cos inverse

Answer 9

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

Negative one over the square root of 1-x^2

Question 10

Derivative of tan inverse

Answer 10

1/1+x^2

One over 1+x^2

Question 11

Derivative of cot inverse

Answer 11

-1/1+x^2

Question 12

Derivative of sec inverse

Answer 12

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

One over the absolute value of X times the square root of X squared minus 1

Question 13

Derivative of csc inverse

Answer 13

• 1/|x|(x^2-1)^1/2

- 1 over the absolute value sign of X times the square root of X squared -1

Question 14

Derivative of a^x

Answer 14

a^x lna

Question 15

Derivative logvax

Answer 15

1/xlna

Question 16

Integral of sin x

Answer 16

-Cosx + C

Question 17

Integral of tanx

Answer 17

-ln|cosx| +C

Question 18

Integral of cscx

Answer 18

-ln|cscx+cotx| + C

Question 19

Integral of csc^2x

Answer 19

-cotx + C

Question 20

Integral of sec x

Answer 20

ln|secx+tanx| + C

Question 21

Integral of secant squared

Answer 21

Tanx + C

Question 22

Integral of Secxtanx

Answer 22

Secx +C

Question 23

Integral of cscxcotx

Answer 23

-cscx + C

Question 24

Integral of x^n

Answer 24

1/n+1 x^n+1