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Math Calculus CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Derivatives of the given function. f ( x , y , z ) = x 2 y 3 + z 4 x = s 2 y = s t 2 z = s 2 t (a) We have to calculate the primary derivatives, ∂ f ∂ x , ∂ f ∂ y , ∂ f ∂ z (b) We have to calculate, ∂ x ∂ s , ∂ y ∂ s , ∂ z ∂ s (c) We have to complete the derivatives ( ∂ f ∂ s ) by chain rule. ∂ f ∂ s = ∂ f ∂ x . ∂ f ∂ x + ∂ f ∂ y . ∂ y ∂ s + ∂ f ∂ z . ∂ z ∂ s Answer should be in terms of independent variable s, t.

Derivatives of the given function. f ( x , y , z ) = x 2 y 3 + z 4 x = s 2 y = s t 2 z = s 2 t (a) We have to calculate the primary derivatives, ∂ f ∂ x , ∂ f ∂ y , ∂ f ∂ z (b) We have to calculate, ∂ x ∂ s , ∂ y ∂ s , ∂ z ∂ s (c) We have to complete the derivatives ( ∂ f ∂ s ) by chain rule. ∂ f ∂ s = ∂ f ∂ x . ∂ f ∂ x + ∂ f ∂ y . ∂ y ∂ s + ∂ f ∂ z . ∂ z ∂ s Answer should be in terms of independent variable s, t.

Solution Summary: The author explains how to determine the derivatives of the given function.

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 15.6, Problem 1E

To determine

Derivatives of the given function.

$\begin{array}{l} f (x, y, z) = x^{2} y^{3} + z^{4} \\ x = s^{2} \\ y = s t^{2} \\ z = s^{2} t \end{array}$

(a) We have to calculate the primary derivatives,

$\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}$

(b) We have to calculate,

$\frac{\partial x}{\partial s}, \frac{\partial y}{\partial s}, \frac{\partial z}{\partial s}$

(c) We have to complete the derivatives $(\frac{\partial f}{\partial s})$ by chain rule.

$\frac{\partial f}{\partial s} = \frac{\partial f}{\partial x} . \frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} . \frac{\partial y}{\partial s} + \frac{\partial f}{\partial z} . \frac{\partial z}{\partial s}$

Answer should be in terms of independent variable s, t.

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Chapter 15.6, Problem 6PQ

Chapter 15.6, Problem 2E

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Chapter 15 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 15.1 - Prob. 1PQ Ch. 15.1 - Prob. 2PQ Ch. 15.1 - Prob. 3PQ Ch. 15.1 - Prob. 4PQ Ch. 15.1 - Prob. 5PQ Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - Prob. 3E Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E

Ch. 15.1 - Prob. 6E Ch. 15.1 - Prob. 7E Ch. 15.1 - Prob. 8E Ch. 15.1 - Prob. 9E Ch. 15.1 - Prob. 10E Ch. 15.1 - Prob. 11E Ch. 15.1 - Prob. 12E Ch. 15.1 - Prob. 13E Ch. 15.1 - Prob. 14E Ch. 15.1 - Prob. 15E Ch. 15.1 - Prob. 16E Ch. 15.1 - Prob. 17E Ch. 15.1 - Prob. 18E Ch. 15.1 - Prob. 19E Ch. 15.1 - Prob. 20E Ch. 15.1 - Prob. 21E Ch. 15.1 - Prob. 22E Ch. 15.1 - Prob. 23E Ch. 15.1 - Prob. 24E Ch. 15.1 - Prob. 25E Ch. 15.1 - Prob. 26E Ch. 15.1 - Prob. 27E Ch. 15.1 - Prob. 28E Ch. 15.1 - Prob. 29E Ch. 15.1 - Prob. 30E Ch. 15.1 - Prob. 31E Ch. 15.1 - Prob. 32E Ch. 15.1 - Prob. 33E Ch. 15.1 - Prob. 34E Ch. 15.1 - Prob. 35E Ch. 15.1 - Prob. 36E Ch. 15.1 - Prob. 37E Ch. 15.1 - Prob. 38E Ch. 15.1 - Prob. 39E Ch. 15.1 - Prob. 40E Ch. 15.1 - Prob. 41E Ch. 15.1 - Prob. 42E Ch. 15.1 - Prob. 43E Ch. 15.1 - Prob. 44E Ch. 15.1 - Prob. 45E Ch. 15.1 - Prob. 46E Ch. 15.1 - Prob. 47E Ch. 15.1 - Prob. 48E Ch. 15.1 - Prob. 49E Ch. 15.1 - Prob. 50E Ch. 15.1 - Prob. 51E Ch. 15.1 - Prob. 52E Ch. 15.1 - Prob. 53E Ch. 15.1 - 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