Each card is a single, complete idea: what it is, the formulas you need, and one worked example. Built to be re-read.
Differentiate a relationship between quantities with respect to time, then substitute the known rates.
Velocity is the derivative of position and acceleration is the derivative of velocity. Speed is |v(t)|.
In an applied problem, f'(a) is the instantaneous rate of change of the output with respect to the input at x = a. A full interpretation names the value, the units, the time/input, and the direction of change.
The units of a derivative are output units divided by input units. The second derivative divides again by the input units, which is why applied second derivatives carry squared units.
Speed is |v(t)|. Compare the signs of velocity and acceleration: matching signs mean the particle is speeding up, opposite signs mean it is slowing down. Positive velocity means motion right/up, negative means left/down.
Displacement is the net change in position over an interval, not the total distance traveled. Average velocity is that net change divided by the elapsed time — an average rate of change, not the average of velocities.
Most related-rates setups come from a standard geometry formula. Treat every variable as a function of t, so differentiating A=lw needs the product rule and a2+b2=c2 generates 2a⋅dtda terms.
Use the tangent line at a convenient point to estimate f at a nearby input. Concave up graphs sit above their tangent line, so the estimate is too low; concave down graphs give an overestimate.
Only after direct substitution gives 00 or ∞∞ may you differentiate the numerator and denominator separately (not with the quotient rule) and re-evaluate the limit. Repeat if the form is still indeterminate.