Because the above expression is equal to the difference The need to define Q at g(a) is analogous to the need to define η at zero.
Similarly, because meters per second, the expression f′(g′(10)) represents the change in pressure at a height of −98 meters per second, which is also nonsense.
However, g(10) is 3020 meters above sea level, the height of the skydiver ten seconds after his jump. The simplest form of the chain rule is for real-valued functions of one real variable.
The chain rule does not appear in any of Leonhard Euler's analysis books, even though they were written over a hundred years after Leibniz's discovery. Assume that t seconds after his jump, his height above sea level in meters is given by .
While it is always possible to directly apply the definition of the derivative to compute the derivative of a composite function, this is usually very difficult.
In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.