Chain rule evaluation
Not what you're looking for? Search our solutions OR ask your own Custom question.
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 March 6, 2023, 1:15 pm ad1c9bdddfhttps://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.
$2.49