Derivatives (functions and inverse)

Question 1

d/dx (x^n)

Answer 1

n(x^n-1)

Question 2

d/dx sin(u)

Answer 2

cos(u) (u’)

Question 3

d/dx cos(u)

Answer 3

-sin(u) (u’)

Question 4

d/dx tan(u)

Answer 4

sec²(u) (u’)

Question 5

d/dx cot(u)

Answer 5

-csc²(u) (u’)

Question 6

d/dx sec(u)

Answer 6

sec(u)tan(u) (u’)

Question 7

d/dx csc(u)

Answer 7

-csc(u)cot(u) (u’)

Question 8

d/dx ln(u)

Answer 8

u’/u

Question 9

d/dx e^u

Answer 9

e^u

Question 10

d/dx sin⁻⁻¹ (u)

Answer 10

u’/(√1-u²)

Question 11

d/dx cos⁻⁻¹(u)

Answer 11

-u’/(√1-u²)

Question 12

d/dx tan⁻⁻¹(u)

Answer 12

u’/(1+u²)

Question 13

d/dx cot⁻⁻¹(u)

Answer 13

-u’/(1+u²)

Question 14

d/dx sec⁻⁻¹(u)

Answer 14

u’/(u √u²-1)

Question 15

d/dx csc⁻⁻¹(u)

Answer 15

-u’/(u √u²-1)

Question 16

d/dx f⁻¹(x)

Answer 16

1/f’(f⁻¹(x))

Question 17

g’(b)

Answer 17

1/f’(a)

Question 18

d/dx 1/u(x)

Answer 18

u’(x)/u(x)^2