Since sine takes on the same value at x and x + 2p, you must restrict the range of arcsin x to make it a well defined function. It is standard to define arcsine to lie between - p / 2 and p / 2. Since holds, arcsin x is only defined for . Arcsin x is a tame looking function, except that its derivative is infinite at . The chain rule states that the derivative of the composite function is the product of the derivative of f and the derivative of g. This is −6.5 °C/km ⋅ 2.5 km/h = −16.25 °C/h . One of the reasons why this computation is possible is because f ′ is a constant function.