Concept

Chain rule

Summary
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\circ g is the function such that h(x)=f(g(x)) for every x, then the chain rule is, in Lagrange's notation, :h'(x) = f'(g(x)) g'(x). or, equivalently, :h'=(f\circ g)'=(f'\circ g)\cdot g'. 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 (that is, y and z are dependent variables), then z depends on x as well, via the intermediate variable y. In this case, the chain rule is expressed as :\frac{dz}{dx} = \frac{dz}{dy} \cdot \frac{dy}{dx}, and : \left.\frac{dz}{dx}\right
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