Rules of Differentiation

Question 1

Sum Rule

Answer 1

d/dx [ƒ(x) + 𝑔(x)] = ƒ’(x) + 𝑔’(x)

Question 2

Difference Rule

Answer 2

d/dx [ƒ(x) - 𝑔(x)] = ƒ’(x) - 𝑔’(x)

Question 3

Constant Multiple Rule

Answer 3

d/dx [kƒ(x)] = kƒ’(x)

Question 4

Power Rule

Answer 4

d/dx [xⁿ] = nxⁿ⁻¹

Question 5

Product Rule

Answer 5

d/dx [ƒ(x)𝑔(x)] = ƒ’(x)𝑔(x) + ƒ(x)𝑔’(x)

Question 6

Quotient Rule

Answer 6

d/dx [ƒ(x)/𝑔(x)] = ƒ’(x)𝑔(x) - ƒ(x)𝑔’(x) / (𝑔(x))²

Question 7

Chain Rule

Answer 7

d/dx [ƒ(𝑔(x))] = ƒ’(𝑔(x)) ∗ 𝑔’(x)