The List

Question 1

Derivative at a point

Answer 1

F’(x)=limx->c (f(x)-f(c))/(x-c)

Question 2

Derivative as a function

Answer 2

F’(x)=lim h->0 (f(x+h)-f(x))/h

Question 3

D/dx(x^n)

Answer 3

nx^n-1

Question 4

D/dx(sinx)

Answer 4

Cosx

Question 5

D/dx(cosx)

Answer 5

-sinx

Question 6

D/dx(e^x)

Answer 6

e^x

Question 7

D/dx(b^x)

Answer 7

b^xlnb

Question 8

D/dx(lnx)

Answer 8

1/x

Question 9

D/dx(uv)

Answer 9

U’v+uv’

Question 10

D/dx(tanx

Answer 10

Sec^2x

Question 11

D/dx(cotx

Answer 11

-csc^2x

Question 12

D/dx(cscx)

Answer 12

-cscxcotx

Question 13

D/dx(secx

Answer 13

Secxtanx

Question 14

D/dx(sin^-1x

Answer 14

1/(1-x^2)^.5

Question 15

D/dx(cos^-1x

Answer 15

-1/(1-x^2)^.5

Question 16

D/dx(tan^-1x

Answer 16

1/(1+x^2)

Question 17

D/dx(cot^-1x

Answer 17

-1/(1+x^2)

Question 18

D/dx(sec^-1x)

Answer 18

1/(|x|(x^2-1)^.5)

Question 19

D/dx(csc^-1)

Answer 19

-1/(|x|(x^2-1)^.5)

Question 20

Chain rule

Answer 20

Take the derivative of the outside fxn while keeping the inside the same. Multiply by the derivative of the inside

Question 21

D/dx(displacement

Answer 21

Velocity

Question 22

D/dx(velocity

Answer 22

Acceleration

Question 23

TRAPRULE

Answer 23

(.5first+all middle+.5last)width

Question 24

Infinite form

Answer 24

X/0 where x=/=0

Question 25

Indeterminate forms

Answer 25

0/0 , 0^0, inf/inf