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Use the chain rule to find d, where First the pieces: d dt dy || || || 2xy + y² x² + 2xy z = x²y + xy², x = -2+t, y=3+t²

Use the chain rule to find d, where First the pieces: d dt dy || || || 2xy + y² x² + 2xy z = x²y + xy², x = -2+t, y=3+t²

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the chain rule to find dz, where dt' First the pieces: дz Əx Əz მყ dx dt dy dt = || || 2xy + y² x² + 2xy End result (in terms of just t): dz dt z=x²y + xy², x = −2+tº,_y=3+ t²
Transcribed Image Text:Use the chain rule to find dz, where dt' First the pieces: дz Əx Əz მყ dx dt dy dt = || || 2xy + y² x² + 2xy End result (in terms of just t): dz dt z=x²y + xy², x = −2+tº,_y=3+ t²
Use the chain rule to find as and ar, where First the pieces: дz ?x ?x მs || дz Ət || ду მ3 And putting it all together: Oz Əs || || || FI Oz ду ?x Ət ду Ət || || ✔ z = x² + xy + y², x = 9s + 2t, y = 3s + 2t x
Transcribed Image Text:Use the chain rule to find as and ar, where First the pieces: дz ?x ?x მs || дz Ət || ду მ3 And putting it all together: Oz Əs || || || FI Oz ду ?x Ət ду Ət || || ✔ z = x² + xy + y², x = 9s + 2t, y = 3s + 2t x
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