derivatives of trig functions and inverse trig functions (hint: the denominators don't change signs)

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 csc(x)

Answer 4

−csc(x)cot(x)

Question 5

d/dx sec(x)

Answer 5

sec(x)tan(x)

Question 6

d/dx cot(x)

Answer 6

−csc^2(x)

Question 7

d/dx sin^-1x (inverse sin)

Answer 7

1/√1-x²

Question 8

d/dx cos^-1x (inverse cos)

Answer 8

-1/√1-x²

Question 9

d/dx tan^-1x (inverse tan)

Answer 9

1/1+x²

Question 10

d/dx csc^-1x (inverse csc)

Answer 10

-1/|x|√x²-1

Question 11

d/dx sec^-1x (inverse sec)

Answer 11

1/|x|√x²-1

Question 12

d/dx cot^-1x

Answer 12

-1/1+x²