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(i) If f(x, y) = sin (ry2) and x³ + y² = 2xy, find expressions for the partial derivatives of/0x and af/ay and the total derivatives df/dx and df/dy in terms of x and y. (In the latter you do not need to simplify your answer.) (::) T

(i) If f(x, y) = sin (ry2) and x³ + y² = 2xy, find expressions for the partial derivatives of/0x and af/ay and the total derivatives df/dx and df/dy in terms of x and y. (In the latter you do not need to simplify your answer.) (::) T

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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part i) please

A 4. (i) If f(x, y) = sin (ry²) and x³ + y² = 2xy, find expressions for the partial derivatives of/0x and af/ay and the total derivatives df/dx and df/dy in terms of x and y. (In the latter you do not need to simplify your answer.) (ii) Let variables x, y and z be linked by the two relationships f(x, y, z) = x³y - z - 1 = 0, g(x, y, z) = x + y² +2³-6=0. Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.
Transcribed Image Text:A 4. (i) If f(x, y) = sin (ry²) and x³ + y² = 2xy, find expressions for the partial derivatives of/0x and af/ay and the total derivatives df/dx and df/dy in terms of x and y. (In the latter you do not need to simplify your answer.) (ii) Let variables x, y and z be linked by the two relationships f(x, y, z) = x³y - z - 1 = 0, g(x, y, z) = x + y² +2³-6=0. Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.
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Step 1: Introduction

To calculate partial derivative of f left parenthesis x comma y right parenthesis with respect  x, we keep the other variable y constant.

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