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