Exam 2

Question 1

d/dx sin x =
d/dx cos x=
d/dx tan x=
d/dx csc x=
d/dx sec x=
d/dx cot x=

Answer 1

cos x
-sinx
sec^2x
-cscxcotx
secxtanx
-csc^2x

Question 2

d/dx lnx=

Answer 2

1/x

Question 3

How to find the derivative of an inverse function at a point when given f(x)

Answer 3

you first derive f(x) then you get the (x,y) of the inverse function and reverse them like (y,x) then the slope of the inverse is the reciprocal

Question 4

sin x/ x
1-cosx/ x

Answer 4

1
0

Question 5

sin (a+b)
sin(a-b)

Answer 5

sin a cos b+ sin b cos a
sin a cos b -sin b cos a

Question 6

cos(a+b)
cos (a-b)

Answer 6

cos a cos b- sin a sin b
cos a cos b + sin a sin b

Question 7

How to find horizontal tangent?

Answer 7

find derivative and equal it to zero

Question 8

ln e^x=
e^lnx=

Answer 8

x

Question 9

d/dx [e^f(x)]=

Answer 9

e^ f(x) x f’(x)

Question 10

(a)^x =
2^pi=

d/dx (a)^u =

Answer 10

e^xna
e^pi (ln2)

(ln a) a^u (du/dx)

Question 11

d/dx log a (x)=

Answer 11

ln x/ ln u

Question 12

d/dx arc sin x =
d/dx arc cos x=

Answer 12

1/ √1-x^2
-1/ √1-x^2

Question 13

d/dx arc tan x=
d/dx arc cot x=

Answer 13

1/1+x^2
-1/1+x^2

Question 14

d/dx arc sec x=
d/dx arc csc x=

Answer 14

1/ |x|√u^2-1
-1/ |x|√u^2-1

Question 15

area of circle
volume of cone
volume of sphere

Answer 15

pi r^2
1/3 pi r^2 h
4/3 pi r^3