Unit 2 & 3 (Chain Rule Theorums, Inverse Derivative Rules, etc.)

Question 1

sinx

Answer 1

cosx

Question 2

cosx

Answer 2

-sinx

Question 3

tanx

Answer 3

sec²x

Question 4

cotx

Answer 4

-csc ²x

Question 5

secx

Answer 5

secx * tanx

Question 6

cscx

Answer 6

-cscx * cotx

Question 7

lnx

Answer 7

1/x

Question 8

logₐx

Answer 8

1/(lna * x)

Question 9

sin⁻¹x

Answer 9

1/(√1-x²)

Question 10

cos⁻¹x

Answer 10

-1/(√1-x²)

Question 11

tan⁻¹x

Answer 11

1/(1+x²)

Question 12

cot⁻¹x

Answer 12

-1/(1+x²)

Question 13

sec⁻¹x

Answer 13

1/(|x|√x²-1)

Question 14

csc⁻¹x

Answer 14

-1/(|x|√x²-1)

Question 15

eˣ

Answer 15

eˣ

Question 16

aˣ

Answer 16

lna * aˣ

Question 17

f * g

Answer 17

f’ * g + g’ * f

Question 18

f/g

Answer 18

(f’ *g - g’ * f)/g²

Question 19

f(g(x))

Answer 19

f’(g(x)) * g’(x)

Question 20

f’(x)

Answer 20

limit as h→0 (f(x + h) - f(x))/h

Question 21

(f⁻¹)’(x)

Answer 21

1/(f’(f⁻¹(x))