Differentiation - Product, Quotient and Chain Rules

We have four rules of differentiation.

1. Sum Rule: \( \frac{\mathrm{d}}{\mathrm{d}x} [\mathrm{f}(x)+\mathrm{g}(x)] = \frac{\mathrm{d}}{\mathrm{d}x} \mathrm{f}(x) + \frac{\mathrm{d}}{\mathrm{d}x} \mathrm{g}(x) \)
2. Product Rule: \( \frac{\mathrm{d}}{\mathrm{d}x} [\mathrm{f}(x) \cdot \mathrm{g}(x)] = \frac{\mathrm{d}}{\mathrm{d}x} \mathrm{f}(x) \cdot \mathrm{g}(x) + \mathrm{f}(x) \cdot \frac{\mathrm{d}}{\mathrm{d}x} \mathrm{g}(x) \)