Standard Derivatives and Integrals

Question 1

Derivative of

xⁿ

Answer 1

nx^n-1

Question 2

Derivative of

e^x

Answer 2

e^x

Question 3

Derivative of

ln x

Answer 3

1 / x

Question 4

Derivative of

sin x

Answer 4

cos x

Question 5

Derivative of

cos x

Answer 5

• sin x

Question 6

Derivative of

tan x

Answer 6

sec² x = 1 / cos² x

Question 7

Derivative of

ln(cos x)

Answer 7

• tan x

Question 8

Derivative of

sin⁻¹ x

Answer 8

1 / √(1−x²)

Question 9

Derivative of

cos^-1 x

Answer 9

• 1 / √ ( 1 - x²)

Question 10

Derivative of

tan⁻¹ x

Answer 10

1 / (1 + x²)

Question 11

Derivative of

sinh x

Answer 11

cosh x

Question 12

Derivative of

cosh x

Answer 12

sinh x

Question 13

Derivative of

tanh x

Answer 13

sech² x = 1 / (cosh² x)

Question 14

Derivative of

sinh^-1 x

Answer 14

1 / √(1 + x²)

Question 15

Derivative of

cosh^-1 x

Answer 15

1 / √( −1 + x²)

Question 16

Derivative of

tanh⁻¹ x

Answer 16

1 / (1−x²)

Question 17

Derivative of

(ax + b)ⁿ

Answer 17

a n (ax + b)^{<em>n</em> - 1}

Question 18

Derivative of

e^{(<em>ax</em> + <em>b</em>)}

Answer 18

a e^{(<em>ax</em> + <em>b</em>)}

Question 19

Derivative of

ln (ax + b)

Answer 19

a / (ax + b)

Question 20

Derivative of

sin (ax + b)

Answer 20

a cos (ax + b)

Question 21

Derivative of

cos (ax + b)

Answer 21

-a sin (ax + b)

Question 22

Derivative of

tan (ax + b)

Answer 22

a sec² (ax + b) = a / cos² (ax + b)

Question 23

Derivative of

ln (cos (ax + b))

Answer 23

-a tan(ax + b)

Question 24

Derivative of

sin⁻¹ (ax + b)

Answer 24

a / √(1 − (ax + b)²)

Question 25

Derivative of cos^-1 (*ax* + *b*)

Answer 25

- *a* / √ (1 − (*ax* + *b*) ²)

Question 26

Derivative of tan⁻¹ (*ax* + *b*)

Answer 26

*a* / (1 + (*ax* + *b*)²)

Question 27

Derivative of sinh (*ax* + *b*)

Answer 27

*a* cosh (*ax* + *b*)

Question 28

Derivative of cosh (*ax* + *b*)

Answer 28

*a* sinh (*ax* + *b*)

Question 29

Derivative of tanh (*ax* + *b*)

Answer 29

*a* sech² (*ax* + *b*) = *a* / (cos² (*ax* + *b*))

Question 30

Derivative of sinh^-1 (*ax* + *b*)

Answer 30

*a* / √(1 + (*ax* + *b*)²)

Question 31

Derivative of cosh^-1 (*ax* + *b*)

Answer 31

*a* / √( -1 + (*ax* + *b*)²)

Question 32

Derivative of tanh⁻¹ (*ax* + *b*)

Answer 32

*a* / (1 − (*ax* + *b*)²)

Question 33

Here, a, b, n are ... and x is the independent variable

Answer 33

constants

Question 34

Here, a, b, n are constants and x is ... .

Answer 34

the independent variable