Derivatives

Question 1

Derivative of 1/x

Answer 1

-1/x^2

Question 2

Derivative of the square root of x

Answer 2

1/(2 • square root of x)

Question 3

Product Rule:

Answer 3

d/dx (u•v) = du • v + u • dv

Question 4

Quotient Rule:

Answer 4

d/dx Hi/Lo = (Lo • dHi - Hi • dLo)/(Lo)^2

Question 5

Sum Rule:

Answer 5

d/dx (u+v) = (du/dx + dv/dx)

Question 6

Difference Rule:

Answer 6

d/dx (u-v) = (du/dx) - (dv/dx)

Question 7

Derivative of e^x

Answer 7

e^x

Question 8

Derivative of lnx

Answer 8

1/x

Question 9

Power Rule:

Answer 9

x^n = nx^n-1

Question 10

Chain Rule:

Answer 10

dy/dx = dy/du • du/dx

Question 11

Derivative of sinx

Answer 11

cosx

Question 12

Derivative of cosx

Answer 12

-sinx

Question 13

Derivative of tanx

Answer 13

sec^2x

Question 14

Derivative of cscx

Answer 14

-cscx • cotx

Question 15

Derivative of secx

Answer 15

secx • tanx

Question 16

Derivative of cotx

Answer 16

-csc^2x

Question 17

d/dx (arcsinx)

Answer 17

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

Question 18

d/dx (arccosx)

Answer 18

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

Question 19

d/dx (arctanx)

Answer 19

1/1 + x^2

Question 20

d/dx (arccotx)

Answer 20

-1 /1 + x^2

Question 21

d/dx (arcsecx)

Answer 21

1/ |x|•(_/x^2 - 1)

Question 22

d/dx (arccscx)

Answer 22

-1/ |x| • (_/x^2 - 1)

Question 23

d/dx logax

Answer 23

1/xlna

Question 24

d/dx a^x

Answer 24

a^x ln a