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Calculating Second-Order Partia Find all the second-order partial d cises 41–50. for wour 41. f(x, y) = x + y + xy

Calculating Second-Order Partia Find all the second-order partial d cises 41–50. for wour 41. f(x, y) = x + y + xy

Calculus: Early Transcendentals
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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Please help with problem #43. Thank you! 

### Calculating Second-Order Partial Derivatives Find all the second-order partial derivatives of the functions in Exercises 41–50. **41.** \( f(x, y) = x + y + xy \) **42.** \( f(x, y) = \sin(xy) \) **43.** \( g(x, y) = x^2 y + \cos y + y \sin x \) **44.** \( h(x, y) = xe^y + y + 1 \) **45.** \( r(x, y) = \ln(x + y) \) **46.** \( s(x, y) = \tan^{-1}\left(\frac{y}{x}\right) \) **47.** \( w = x^2 \tan(xy) \) **48.** \( w = y e^{x^2 - y} \) **49.** \( w = x \sin(x^2 y) \) **50.** \( w = \frac{x - y}{x^2 + y} \) **51.** \( f(x, y) = x^2 y^3 - x^4 + y^5 \) **52.** \( g(x, y) = \cos(x^2) - \sin(3y) \) **53.** \( z = x \sin(2x - y^2) \) **54.** \( z = x e^{x/y^2} \)
Transcribed Image Text:### Calculating Second-Order Partial Derivatives Find all the second-order partial derivatives of the functions in Exercises 41–50. **41.** \( f(x, y) = x + y + xy \) **42.** \( f(x, y) = \sin(xy) \) **43.** \( g(x, y) = x^2 y + \cos y + y \sin x \) **44.** \( h(x, y) = xe^y + y + 1 \) **45.** \( r(x, y) = \ln(x + y) \) **46.** \( s(x, y) = \tan^{-1}\left(\frac{y}{x}\right) \) **47.** \( w = x^2 \tan(xy) \) **48.** \( w = y e^{x^2 - y} \) **49.** \( w = x \sin(x^2 y) \) **50.** \( w = \frac{x - y}{x^2 + y} \) **51.** \( f(x, y) = x^2 y^3 - x^4 + y^5 \) **52.** \( g(x, y) = \cos(x^2) - \sin(3y) \) **53.** \( z = x \sin(2x - y^2) \) **54.** \( z = x e^{x/y^2} \)
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