Addition and Subtraction Rule

Addition and Subtraction Rule

For each function below, find \(\mathrm f\prime(x)\).

Addition and Subtraction Rule

\(\frac{\mathrm{d}}{\mathrm{d}x}(kx^n + qx^m) = k\frac{\mathrm{d}}{\mathrm{d}x}(x^n) + q\frac{\mathrm{d}}{\mathrm{d}x}(x^m) = knx^{n-1} + qmx^{m-1}\), where \(k\) and \(q\) are constants.

  1. \(\mathrm{f}(x) = 6x^5 - x^6 - 10\)
  2. \(\mathrm{f}(x) = 2 - 5x^3 - 4\sqrt{x}\)
  3. \(\mathrm{f}(x) = 6x - 5x^2 + 3\sqrt{x}\)

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Answer:(a) \(30x^4-6x^5\) (b) \(-15x^2-2x^{-\frac{1}{2}}\) (c) \(6-10x+\frac{3}{2}x^{-\frac{1}{2}}\)

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