Derivatives of inverse functions

Question 1

d/dx sin^-1x

Answer 1

1/√(1-x^2)

Question 2

d/dx cos^-1x

Answer 2

-1/√(1-x^2)

Question 3

d/dx tan^-1x

Answer 3

1/1+x^2

Question 4

d/dx csc^-1x

Answer 4

-1/|x|√(x^2-1)

Question 5

d/dx sec^-1x

Answer 5

1/|x|√(x^2-1)

Question 6

d/dx cot^-1x

Answer 6

-1/1+x^2

Question 7

d/dx a^x

Answer 7

a^x * ln a

Question 8

d/dx loga x

Answer 8

1/(x*ln a)