2 How this connects to your other standards

Differentiation is not sealed inside 91578. Read this first if you are also taking one of the standards below.

How this connects

The most direct links, roughly in order of how often they actually come up:

Integration methods (91579): the inverse operation Differentiation and integration undo each other — the Fundamental Theorem of Calculus is the formal statement of that. Recognising a derivative on sight is what lets you spot the antiderivative of a similar-looking expression, and the same standard derivatives (trig, e^x, ln x) are read in both directions across the two papers. Physics: Mechanical Systems (91524): velocity and acceleration ARE derivatives Velocity is the derivative of displacement; acceleration is the derivative of velocity. Every kinematics problem in that standard is a differentiation problem wearing physics units. Simple harmonic motion is the differential equation d²x/dt² = −ω²x, and differentiating x = A cos(ωt) twice with the chain rule is exactly how that result is proved. Trigonometric methods (91575): the identities you differentiate Differentiating a trig product or a composite trig function (sin³x·cos x, cos(2x)) is far faster once a double-angle or Pythagorean identity has simplified it first. The identities are taught there; you use them here to make a derivative manageable before you even start applying a rule. Linear programming (91574): a different method for a similar-looking question Both standards can ask you to maximise or minimise something. Linear programming finds the optimum at a VERTEX of a feasible region built from straight-line constraints; differentiation finds it where a smooth function's gradient is zero. Reading which kind of problem you are given — straight-line constraints, or one continuous function — decides which method applies. ✓

The big picture in one sentence

Differentiation gives you the rate of change and the shape of a curve; integration (91579) reverses that to recover area, volume and total change; trigonometric methods (91575) supply the identities that keep trig derivatives manageable; and the same optimisation IDEA — find where a quantity is largest or smallest — reappears with a completely different METHOD in linear programming (91574).

Practice for this standard covers the whole topic — flashcards and quiz.