The part of high school mathematics you should master before learning differential calculus are the basics of algebra. 

1. **Functions** Functions are the fundamental objects upon which the derivative acts, so you should be intimately familiar with the nature and behaviour of polynomials, rational fucntions, and exponential functions (especially $f(x) = a \cdot e^{(b \cdot x)}$).
2. **Factorisation** Knowing the rules of factorisation is essential to manipulating functions, so you should be familiar with the basic factorisation patterns, including grouping, GCF, sum-of-cubes, difference-of-cubes, and difference-of-squares.
3. **Limits** The foundations of calculus are built on limits, and while it isn't necessary to understand limits to understand calculus, school course in calculus usually require work with limits, and differential calculus has many applications to the evaluation of limits.

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