Derivative Rules + Trig Rules

Question 1

d/dx [sin x]

Answer 1

cos x

Question 2

d/dx [ cos x]

Answer 2

-sin x

Question 3

d/dx [tan x]

Answer 3

sec^2 x

Question 4

d/dx [sec x]

Answer 4

sec x tan x

Question 5

d/dx [csc x]

Answer 5

csc x cot x

Question 6

d/dx [cot x]

Answer 6

csc^2 x

Question 7

d/dx [arcsin x]

Answer 7

1/(root 1-x^2)

Question 8

d/dx [arccos x]

Answer 8

-1/(root 1-x2)

Question 9

d/dx [arctan x]

Answer 9

1/(1 + x^2)

Question 10

d/dx [arccot x]

Answer 10

-1/(1 + x^2)

Question 11

d/dx [arcsec x]

Answer 11

1/(x root x^2 -1)

Question 12

d/dx [arccsc x]

Answer 12

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

Question 13

tan

Answer 13

sin/cos

Question 14

sec

Answer 14

1/cos

Question 15

csc

Answer 15

1/sin

Question 16

cot

Answer 16

cos/sin OR 1/tan

Question 17

sin^2 + cos2

Answer 17

1

Question 18

sin^2

Answer 18

1 - cos^2

Question 19

cos^2

Answer 19

1 - sin^2

Question 20

limit definition of derivative in terms of a

Answer 20

f(x) - f(a) / (x-a)

Question 21

limit definition of derivative in terms of h

Answer 21

f(x+h) - f(x) / h

Question 22

product rule

Answer 22

f’(x)g(x) + g’(x)f(x)

Question 23

quotient rule

Answer 23

f’(x)g(x) - g’(x)f(x) / g(x)^2

Question 24

chain rule

Answer 24

f’(g(x)) * g’(x)