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Wize AP Calculus (BC) Textbook > Differentiation 1: Basics & Fundamental Properties

Differentiation Laws

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Differentiation Laws

Let ff and gg be two differentiable functions and kk be a constant. We have the following rules:

  1. Sum Rule: ddx(f(x)+g(x))=dfdx+dgdx\dfrac{d}{dx}\Big(f(x)+g(x)\Big)=\dfrac{df}{dx}+\dfrac{dg}{dx}
  2. Difference Rule: ddx(f(x)−g(x))=dfdx−dgdx\dfrac{d}{dx}\Big(f(x)-g(x)\Big)=\dfrac{df}{dx}-\dfrac{dg}{dx}
  3. Constant Multiple Rule: ddx(kf(x))=kdfdx\dfrac{d}{dx}\Big(kf(x)\Big)=k\dfrac{df}{dx}