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    Chain rule evaluation

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    You are given the function w=yz/x, where x=θ^2, y=r+θ and z=r-θ. Find ∂w/∂θ.

    a) using the appropriate chain rule

    b) converting w to a function of r,θ before differentiating.

    Which of the above is quicker?

    © BrainMass Inc. brainmass.com February 24, 2021, 2:16 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/chain-rule-evaluation-10494

    Solution Preview

    a.)
    partial derivative:
    del(w)/del(Q) = yz.del(1/x)/del(Q) + (y/x).del(z)/del(Q) + (z/x).del(y)/del(Q)
    here, read Q as theta.
    => del(w)/del(Q) = (-yz/x^2)*del(x)/del(Q)+(y/x).del(z)/del(Q) + (z/x).del(y)/del(Q)
    => del(w)/del(Q) ...

    Solution Summary

    This looks at two ways to differentiate a function: using a chain rule or converting the function. It then determines which is the quicker method.

    $2.19

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