The derivative questions on the gaokao lean on execution more than insight. Get the mechanical rules airtight and you will out-score half the class before touching an application problem.
Memorize, cold: the derivatives of xⁿ, eˣ, ln x, sin x, cos x, and tan x. The chain rule, product rule, and quotient rule. Say them out loud once a day for a week and they stop being a bottleneck.
Applications almost always take one of three shapes: find the tangent line at a point, find intervals of monotonicity, or find extrema. Practice one of each per day.
The classic trap in monotonicity questions is forgetting to check the endpoints of the interval and the points where the derivative is undefined. Build the habit of listing every candidate before deciding which is the maximum.
For extrema on a closed interval, always compute f at both endpoints as well as at every interior critical point. Skipping this step is the most common lost mark on this topic.