Inverse Trig

Question 1

y = arcsin (x), y = arcsin (u)

Answer 1

y’ = 1/cos(arcsin(x)), y’ = u’/sqrt(1-u^2)

Question 2

y = arccos (x), y = arccos (u)

Answer 2

y’ = -1 / sqrt(1-x^2), y’ = -u’ / sqrt(1-u^2)

Question 3

y = arctan (x), y = arctan (u)

Answer 3

y’ = 1/1+x^2, y’ = u’ / 1+u^2

Question 4

y = arcsec (x), y = arcsec (u)

Answer 4

y’= 1/|x|sqrt(x^2-1), y’= u’/|u|sqrt(u^2-1)

Question 5

y = arccsc(x), y = arccsc(u)

Answer 5

y’=-1/|x|sqrt(x^2-1), y’=-u’/|u|sqrt(u^2-1)

Question 6

y = arccot (x), y = arccot (u)

Answer 6

y’ = -1/1+x^2, y’ = -u’/1+u^2