If G is a function of s, and s is a function of z, what is the Chain Rule formula for the derivative of the composition function?

Question

If G is a function of s, and s is a function of z, what is the Chain Rule formula for the derivative of the composition function?

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Piper 2 weeks 2021-09-08T15:51:55+00:00 1 Answer 0

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    2021-09-08T15:53:50+00:00

    Answer:

    (G(s(z)))'=G'(s(z))\cdot s'(z))

    Step-by-step explanation:

    If G is a function of s, and s is a function of z, then the composition function is :

    (G\circ s)(z)=G(s(z))

    This is a function of a function. So we apply the chain rule to different the outer function multiply by the derivative of the inner function.

    We take the first derivative to obtain:

    (G(s(z)))'=G'(s(z))\cdot s'(z))

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