Let z(x, y) Calculate дz მs дz 2t = дz მs & 7х2 + y² where x = s + 8t & y = дz St by first finding ?х ду дх 3 ?s' is t 1 & - 78 + 9t. ду St and using the chain rule.
Let z(x, y) Calculate дz მs дz 2t = дz მs & 7х2 + y² where x = s + 8t & y = дz St by first finding ?х ду дх 3 ?s' is t 1 & - 78 + 9t. ду St and using the chain rule.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Let \( z(x, y) = -7x^2 + y^2 \) where \( x = s + 8t \) and \( y = -7s + 9t \).
Calculate \(\frac{\partial z}{\partial s}\) and \(\frac{\partial z}{\partial t}\) by first finding \(\frac{\partial x}{\partial s}\), \(\frac{\partial y}{\partial s}\), \(\frac{\partial x}{\partial t}\), and \(\frac{\partial y}{\partial t}\) and using the chain rule.
\[
\frac{\partial z}{\partial s} = \underline{\hspace{6cm}}
\]
\[
\frac{\partial z}{\partial t} = \underline{\hspace{6cm}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f1031d2-2e66-499b-af2c-dad17e4bc047%2F5be56d32-d6b1-409f-9992-5dcb037e991c%2Fejs2fwl_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( z(x, y) = -7x^2 + y^2 \) where \( x = s + 8t \) and \( y = -7s + 9t \).
Calculate \(\frac{\partial z}{\partial s}\) and \(\frac{\partial z}{\partial t}\) by first finding \(\frac{\partial x}{\partial s}\), \(\frac{\partial y}{\partial s}\), \(\frac{\partial x}{\partial t}\), and \(\frac{\partial y}{\partial t}\) and using the chain rule.
\[
\frac{\partial z}{\partial s} = \underline{\hspace{6cm}}
\]
\[
\frac{\partial z}{\partial t} = \underline{\hspace{6cm}}
\]
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