Uses of the Power Rule (4.1.3)

Question 1

• The power rule states that if N is a rational number, then the function f(x) = x^N is differentiable and f’(x) = Nx^(N-1).

Answer 1

• The power rule states that if N is a rational number, then the function f(x) = x^N is differentiable and f’(x) = Nx^(N-1).

Question 2

• Given a differentiable function f and a constant c, the constant multiple rule states that [c * f(x)]’ = c[f’(x)].

Answer 2

• Given a differentiable function f and a constant c, the constant multiple rule states that [c * f(x)]’ = c[f’(x)].

Question 3

• Given two differentiable functions f and g, the sum rule states that [f(x) + g(x)]’ = f’(x) + g’(x).

Answer 3

• Given two differentiable functions f and g, the sum rule states that [f(x) + g(x)]’ = f’(x) + g’(x).