Question

Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector. f(x,y) = ln (8 + 3x^2 + 2y^2) ; P(-3,1); <1,3> The directional derivative is

          Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector.
f(x,y) = ln (8 + 3x^2 + 2y^2) ; P(-3,1); <1,3>
The directional derivative is

Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector.
f(x,y) = ln (8 + 3x^2 + 2y^2) ; P(-3,1); <1,3>
The directional derivative is

Added by Tracy D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

10/04/2023

Step 1

∂f/∂x = (1/(8+3x^2+2y^2)) * (6x) ∂f/∂y = (1/(8+3x^2+2y^2)) * (4y) So, at point P(-3,1), we have: ∇f(-3,1) = (∂f/∂x, ∂f/∂y) = (6/19, 4/19) Show more…

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Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector. f(x,y) = ln (8 + 3x^2 + 2y^2) ; P(-3,1); <1,3> The directional derivative is