Chain rule

Formula in calculus

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions z and y in terms of the derivatives of z and y. More precisely, if h = z ∘ y {\displaystyle h=z\circ y} is the composition such that h ( x) = z ( y ( x)) {\displaystyle h(x)=z(y(x))} for every x, then the chain rule is, in Lagrange's notation, h ′ ( x) = z ′ ( y ( x)) y ′ ( x) . {\displaystyle h'(x)=z'(y(x))y'(x).} or, equivalently, h ′ = ( z ∘ y) ′ = ( z ′ ∘ y) ⋅ y ′ .

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