What is Chain rule?

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if h = f ∘ g {\displaystyle h=f\circ g} is the function such that h = f ] {\displaystyle h=f]} for every x, then the chain rule is, in Lagrange's notation,

or, equivalently,

The chain rule may also be expressed in Leibniz's notation. If a variable z depends on the variable y, which itself depends on the variable x , then z depends on x as well, via the intermediate variable y. In this case, the chain rule is expressed as

and