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Chain rule evaluation

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You are given the function w=yz/x, where x=&#952;^2, y=r+&#952; and z=r-&#952;. Find &#8706;w/&#8706;&#952;.

a) using the appropriate chain rule

b) converting w to a function of r,&#952; before differentiating.

Which of the above is quicker?

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.

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)
=> 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) ...

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Education
• MSc , Pune University, India
• PhD (IP), Pune University, India
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