Trig Derivatives

Question 1

Dx (sin x)

Answer 1

cos x

Question 2

Dx (cos x)

Answer 2

-sin x

Question 3

Dx (tan x)

Answer 3

sec^2 x

Question 4

Dx (cot x)

Answer 4

-csc^2 x

Question 5

Dx (sec x)

Answer 5

sec x tan x

Question 6

Dx (csc x)

Answer 6

-csc x cot x

Question 7

Dx (ln x)

Answer 7

1/x for x > 0

Question 8

Dx (log_a x)

Answer 8

1 / (x ln a) for x > 0

Question 9

Dx (ln |x|)

Answer 9

1/x for x != 0

Question 10

arcsin

Answer 10

1 / √(1 - x²)

Question 11

arccos

Answer 11

-1 / √(1 - x²)

Question 12

arctan

Answer 12

1 / (1 + x²)

Question 13

arccot

Answer 13

-1 / (1 + x²)

Question 14

arcsec

Answer 14

1 / x√(x² - 1)

Question 15

arccsc

Answer 15

-1 / x√(x² - 1)

Question 16

hyperbolic derivatives

Answer 16

same as normal trig, but left side = postive, right = negative

Question 17

arcsinh

Answer 17

1 / √(x² + 1)

Question 18

arccosh

Answer 18

1 / √(x² - 1)

Question 19

arctanh

Answer 19

1 / (1 - x²) ; |x| < 1

Question 20

arccoth

Answer 20

1 / (1 - x²) ; |x| > 1

Question 21

arcsech

Answer 21

-1 / x√(1 - x²)

Question 22

arccsch

Answer 22

-1 / |x|√(x² + 1)