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Compute all the first partial derivatives for the following functions: (a) f(x₁, x₂) = x₁x²+2x₁ - 7 (b) g(x₁, x₂) = x₁ + x2 sin 2x₁ (c) h(x, y) = xe²+2y + y² (d) f(s, t) = (1 + 2s² + t²) 21 3

Compute all the first partial derivatives for the following functions: (a) f(x₁, x₂) = x₁x²+2x₁ - 7 (b) g(x₁, x₂) = x₁ + x2 sin 2x₁ (c) h(x, y) = xe²+2y + y² (d) f(s, t) = (1 + 2s² + t²) 21 3

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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1. Compute all the first partial derivatives for the following functions: (a) f(x₁, x₂) = x₁x²+2x₁ - 7 (b) g(x₁, x₂) = x₁ + x₂ sin 2x₁ (c) h(x,y) = xe* +23 tỷ (d) f(s, t) = (1 + 2s² + t²) (e) g(0, y) = cos(0 - 34) (f) f(x, y) = x³, x>0 (g) g(x₁, x2, 3) = x1x2x3 (h) u(x, y, z) = xye³+² +5 (i) v(x, y, z) = ln(x² + y² + z²+3) (j) pr, 0, y) = r sin cosy. 2. Compute all the second partial derivatives of the functions in Exercise 1.
Transcribed Image Text:1. Compute all the first partial derivatives for the following functions: (a) f(x₁, x₂) = x₁x²+2x₁ - 7 (b) g(x₁, x₂) = x₁ + x₂ sin 2x₁ (c) h(x,y) = xe* +23 tỷ (d) f(s, t) = (1 + 2s² + t²) (e) g(0, y) = cos(0 - 34) (f) f(x, y) = x³, x>0 (g) g(x₁, x2, 3) = x1x2x3 (h) u(x, y, z) = xye³+² +5 (i) v(x, y, z) = ln(x² + y² + z²+3) (j) pr, 0, y) = r sin cosy. 2. Compute all the second partial derivatives of the functions in Exercise 1.
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