Inverse trig functions and their derivatives

Question 1

d/dx(sinx)

Answer 1

cosx

Question 2

d/dx(tanx)

Answer 2

sec^2x

Question 3

d/dx(secx)

Answer 3

tanxsecx

Question 4

d/dx(cosx)

Answer 4

-sinx

Question 5

d/dx(cotx)

Answer 5

-csc^2x

Question 6

d/dx(cscx)

Answer 6

-cotxcscx

Question 7

limit as x approaches 0 of sinx/x

Answer 7

1

Question 8

limit as x approaches 0 of tanx/x

Answer 8

1

Question 9

limit as x approaches 0 of (1-cosx)/(x^2)

Answer 9

1/2

Question 10

d/dx(arcsin)

Answer 10

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

Question 11

d/dx(arctan)

Answer 11

1/(1+x^2)

Question 12

d/dx(arcsec)

Answer 12

1/(absolute value of x)(sqrtx^2-1)

Question 13

d/dx(arc cos)

Answer 13

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

Question 14

d/dx(arc cot)

Answer 14

-1/(1+x^2)

Question 15

d/dx(arc csc)

Answer 15

-1/(absolute value)(sqrt(x^2-1))