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(a) Compute the directional derivative of f(x, y) = xy² + x³y at the point (4, -2) in the direction û = √(1,3).

(a) Compute the directional derivative of f(x, y) = xy² + x³y at the point (4, -2) in the direction û = √(1,3).

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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1. (a) Compute the directional derivative of f(x, y) = xy² + x³y at the point (4, -2) in the direction û = (1,3). 10 (b) Find the equation of the tangent plane to the surface z = f(x, y) = x² + y², at the point (1, 2, 5), in the form ax +by+cz = d. (c) If x, y and z are linked by the formula x² + y = ez determine z and Zy via implicit differentiation and use (one of) these to show that Zxx 2z(yez - x²)² + 8x²z(yeyz - x²) — 4x²y²z²eyz (yeyz - x²)³
Transcribed Image Text:1. (a) Compute the directional derivative of f(x, y) = xy² + x³y at the point (4, -2) in the direction û = (1,3). 10 (b) Find the equation of the tangent plane to the surface z = f(x, y) = x² + y², at the point (1, 2, 5), in the form ax +by+cz = d. (c) If x, y and z are linked by the formula x² + y = ez determine z and Zy via implicit differentiation and use (one of) these to show that Zxx 2z(yez - x²)² + 8x²z(yeyz - x²) — 4x²y²z²eyz (yeyz - x²)³
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