Derivative Rules

Question 1

Sum Rule: d/dx [f(x) + g(x)] = ?

Answer 1

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

Question 2

Difference Rule: d/dx [f(x) - g(x)] = ?

Answer 2

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

Question 3

Constant Multiple Rule:
d/dx [c ⋅ f(x)] = ?

Answer 3

c ⋅ d/dx [f(x)]

Question 4

Power Rule:
d/dx (x^n) = ?

Answer 4

n ⋅ x^(n - 1)

Question 5

What is the derivative of y = mx + b ?

Answer 5

The slope, m

Question 6

What is d/dx (2x^4) ?

Answer 6

8x^3

Question 7

What is d/dx (6x) ?

Answer 7

6

Question 8

Constant rule: d/dx (c) = ?

Answer 8

0

Question 9

What is d/dx (3x^2 + 5) ?

Answer 9

d/dx (3x^2) + d/dx (5)
6x + 0
6x

Question 10

Product rule: d/dx (fg) = ?

Answer 10

g ⋅ d/dx(f) + f ⋅ d/dx(g)

Question 11

d/dx (e^x) = ?

Answer 11

e^x

Question 12

d/dx (a^x) = ?

Answer 12

ln(a) ⋅ a^x

Question 13

Quotient rule: d/dx(f/g) = ?

Answer 13

(f ⋅ g’ - g ⋅ f’)/g^2

Question 14

Chain rule: d/dx (f ∘ g) = ?

Answer 14

(f’ ∘ g) ⋅ g’