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:
  $$\frac{d}{dx}[x^n] = nx^{n-1}$$