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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?

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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)
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 provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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