gallimoretl gallimoretl
  • 14-03-2020
  • Mathematics
contestada

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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kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 22-03-2020

Answer:

[tex](G(s(z)))'=G'(s(z))\cdot s'(z))[/tex]

Step-by-step explanation:

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

[tex](G\circ s)(z)=G(s(z))[/tex]

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:

[tex](G(s(z)))'=G'(s(z))\cdot s'(z))[/tex]

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