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An example using the chain rule

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Let f: R^3 --> R^2 by given by

f((x,y,z)) = (x^2 + y^2*z^2 + y*z^2)

and let g: R^2 --> R^2 be given by

g((u,v)) = (log(1 + u^2v^2), u^3v)

Use the Chain Rule to compute (g o f)' at (1,0,1)

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Solution Summary

This solution uses the chain rule to calculate the partial derivatives of the composition of two functions of several variables.