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Let f(x, y, z) = x³y + z5 and x = 5, y = st4, and z = st. (a) Calculate the primary derivatives of of of > (Use symbolic notation and fractions where needed.)

Let f(x, y, z) = x³y + z5 and x = 5, y = st4, and z = st. (a) Calculate the primary derivatives of of of > (Use symbolic notation and fractions where needed.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 12CR
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## Problem Statement Let \( f(x, y, z) = x^5 y^5 + z^5 \) and \( x = s^5 \), \( y = st^4 \), and \( z = s^5 t \). ### (a) Calculate the primary derivatives \(\frac{\partial f}{\partial x}\), \(\frac{\partial f}{\partial y}\), \(\frac{\partial f}{\partial z}\). (Use symbolic notation and fractions where needed.) ### Solution: \[ \frac{\partial f}{\partial x} = \boxed{} \] \[ \frac{\partial f}{\partial y} = \boxed{} \] \[ \frac{\partial f}{\partial z} = \boxed{} \]
Transcribed Image Text:## Problem Statement Let \( f(x, y, z) = x^5 y^5 + z^5 \) and \( x = s^5 \), \( y = st^4 \), and \( z = s^5 t \). ### (a) Calculate the primary derivatives \(\frac{\partial f}{\partial x}\), \(\frac{\partial f}{\partial y}\), \(\frac{\partial f}{\partial z}\). (Use symbolic notation and fractions where needed.) ### Solution: \[ \frac{\partial f}{\partial x} = \boxed{} \] \[ \frac{\partial f}{\partial y} = \boxed{} \] \[ \frac{\partial f}{\partial z} = \boxed{} \]
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