Derivatives

Question 1

What is the derivative of the function f(x) = sin (x)

Answer 1

If f(x) = sin (x), then f’(x) = cos (x)

Question 2

What is the derivative of the function f(x) = cos (x)?

Answer 2

If f(x) = cos (x), then f’(x) = -sin (x)

Question 3

What is the derivative of the function f(x) = tan (x)?

Answer 3

If f(x) = tan (x), then f’(x) = sec²(x)

Question 4

What is the derivative of the function f(x) = ln (x)?

Answer 4

If f(x) = ln (x), then f’(x) = 1/x

Question 5

What is the formula for the circumference of a circle?

Answer 5

Circumference = 2πr

Question 6

What is the product rule for derivatives?

Answer 6

f’(x) = g(x) h’(x) + h(x) g’(x)

Question 7

Answer 7

Question 8

What is the derivative of f(x) = cot (x)?

Answer 8

If f(x) = cot (x), then f’(x) = -csc²(x)

Question 9

What is the derivative of the function f(x) = cot (x)?

Answer 9

If f(x) = cot (x), then f’(x) = -csc² (x)

Question 10

What is the derivative of the function f(x) = sec (x)?

Answer 10

If the function f(x) = sec (x), then f’(x) = sec (x) tan (x)

Question 11

What is the derivative of the function f(x) = csc (x)?

Answer 11

If the function is f(x) = csc (x), then f’(x) = -csc (x) cot (x)

Question 12

What is the Pythagorean Theorem?

Answer 12

A² + B² = C²

sin²(x) + cos²(x) = 1

Question 13

What is the formula for the surface area of a sphere?

Answer 13

SA = 4πr²

Question 14

What is the derivative of the function f(x) = a^x?

Answer 14

If the function is f(x) = a^x, then f’(x) = a^x ln a

Question 15

What is the Taylor or linear approximation of a function?

Answer 15

f(x) = f(a) + f’(a)(x-a)

Question 16

Factor difference of squares. a² - b²

Answer 16

a² - b² = (a + b)(a - b)

Question 17

Factor a difference of cubes, a³ - b³

Answer 17

a³ - b³ = (a - b)(a² + ab + b²)

Question 18

Factor a sum of cubes, a³ + b³

Answer 18

a³ + b³ = (a + b)(a² - ab + b²)