Differentiation Formulas

Question 1

d/dx k

Answer 1

0

Question 2

d/dx [f(x) +/- g(x)]

Answer 2

f’(x) +/- g’(x)

Question 3

d/dx [k • f(x)]

Answer 3

k • f’(x)

Question 4

d/dx [f(x)g(x)] = dy/dx = y

Answer 4

f(x)g’(x) + g(x)f’(x) = dy/du • du/dx = f(u)

Question 5

d/dx [f(x)/g(x)]

Answer 5

[g(x)f’(x) - f(x)g’(x)] / [g(x)]²

Question 6

d/dx f(g(x))

Answer 6

f’(g(x)) • g’(x)

Question 7

d/dx x^n

Answer 7

nx^(n-1)

Question 8

d/dx sin(x)

Answer 8

cos(x)

Question 9

d/dx cos(x)

Answer 9

-sin(x)

Question 10

d/dx tan(x)

Answer 10

sec²(x)

Question 11

d/dx sec(x)

Answer 11

sec(x) • tan(x)

Question 12

d/dx csc(x)

Answer 12

• csc(x) • cot(x)

Question 13

d/dx cot(x)

Answer 13

• csc²(x)

Question 14

d/dx e^x

Answer 14

e^x

Question 15

d/dx a^x

Answer 15

a^x • ln(a)

Question 16

d/dx ln|x|

Answer 16

1/x

Question 17

d/dx arcsin(x) = d/dx sin-¹(x)

Answer 17

1/ √(1 - x²)

Question 18

d/dx arccos(x) = d/dx cos-¹(x)

Answer 18

-1 / √(1 - x²)

Question 19

d/dx arctan(x) = d/dx tan-¹(x)

Answer 19

1 / (x² + 1)

Question 20

d/dx arccot(x) = d/dx cot-¹(x)

Answer 20

-1 / (x² + 1)

Question 21

d/dx arcsec(x) = d/dx sec-¹(x)

Answer 21

1 / [|x|√(x² - 1)]

Question 22

d/dx arccsc(x) = d/dx csc-¹(x)

Answer 22

-1 / [|x|√(x² - 1)]