3.1 | Powers and Polynomials


Properties of Derivatives:If \(f(x)\) and \(g(x)\) are differentiable at \(x\) and \(c\) is a constant, then

  • Constant Multiplier Rule:
    $$\frac{d}{dx}[c \cdot f(x)] = c \cdot \frac{d}{dx}[f(x)]$$
  • Sum/Difference Rule:
    $$\frac{d}{dx}[f(x) \pm g(x)] = \frac{d}{dx}[f(x)] \pm \frac{d}{dx}[g(x)]$$
Basic Differentiation Rules: Let \(c\) be a constant.

  • Constant Rule:
    $$ \frac{d}{dx}[c] = 0$$
  • Power Rule:
    $$\frac{d}{dx}[x^n] = nx^{n-1}$$

E 3.1 Exercises