can you please provide explanations (i) If f (x, y) = sin (ry2) and x³ + y² = 2xy, find expressions for the partial derivatives of/0x andaf/ay and the total derivatives df/dx and df/dy in terms of x and y. (In the latter you do notneed to simplify your answer.)

If , then to find the expressions for the partial derivatives and the total derivatives in terms…

Answered: (i) If f(x, y) = sin (xy2) and x³ + y²…

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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can you please provide explanations

(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.)

Expert Solution

Step 1: Define the problem.

If $straight f open parentheses straight x comma space straight y close parentheses equals sin open parentheses xy squared close parentheses space and space straight x cubed plus straight y squared equals 2 xy$ , then to find the expressions for

the partial derivatives $fraction numerator partial differential straight f over denominator partial differential straight x end fraction space and space fraction numerator partial differential straight f over denominator partial differential straight y end fraction$ and the total derivatives $df over dx space and space df over dx$

in terms of $straight x space and space straight y$ .