AP Calc

Question 1

sin^2 x + cos^2 x

Answer 1

1

Question 2

sin 2x

Answer 2

2sinxcosx

Question 3

d/dx tanx

Answer 3

sec^2 x

Question 4

d/dx cotx

Answer 4

-csc^2 x

Question 5

d/dx secx

Answer 5

secxtanx

Question 6

d/dx cscx

Answer 6

-cscxcotx

Question 7

d/dx a^x

Answer 7

a^x lna

Question 8

d/dx loga x

Answer 8

1/xlna

Question 9

d/dx arcsinx

Answer 9

1/sqrt(1-x^2)

Question 10

d/dx arccosx

Answer 10

-1/sqrt(1-x^2)

Question 11

d/dx arctanx

Answer 11

1/1+x^2

Question 12

d/dx arccotx

Answer 12

-1/1+x^2

Question 13

d/dx arcsecx

Answer 13

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

Question 14

d/dx arccscx

Answer 14

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

Question 15

Derivative (limit definition)

Answer 15

lim h->0 f(x+h)-f(x) / h

Question 16

Arc length (Cartesian)

Answer 16

Int a->b sqrt(1+(dy/dx)^2)

Question 17

Speed

Answer 17

Sqrt(x’^2+y’^2)

Question 18

Distance traveled

Answer 18

Int a->b sqrt(x’^2+y’^2)

Question 19

Arc length (parametric)

Answer 19

Int a->b sqrt((x’)^2 + (y’)^2)

Question 20

Trapezoidal approximation

Answer 20

1/2(w(b1+b2) + w(b2+b3) …)

Question 21

Fraction decomposition

Answer 21

Ky(L-y) = L / 1+Ce^-Lkt

Question 22

Washer method

Answer 22

pi * Int R(x)^2 - r(x)^2

Question 23

Shell method

Answer 23

2pi * Int r(x)h(x)

Question 24

Polar area

Answer 24

1/2 Int r^2