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 + x^2 + 3y^2) ; P(- 3,1); <1,1> Find the gradient of f(x,y) = ln (8 + x^2 + 3y^2) . ?f(x,y) = < , > The directional derivative is . (Type an exact answer, using radicals as needed.)

          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 + x^2 + 3y^2) ; P(- 3,1); <1,1>
Find the gradient of f(x,y) = ln (8 + x^2 + 3y^2) .
?f(x,y) = < , >
The directional derivative is .
(Type an exact answer, using radicals as needed.)

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 + x^2 + 3y^2) ; P(- 3,1); <1,1>
Find the gradient of f(x,y) = ln (8 + x^2 + 3y^2) .
?f(x,y) = < , >
The directional derivative is .
(Type an exact answer, using radicals as needed.)

Added by Josefina M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert William Semus

08/09/2023

Step 1

We can do this by taking the derivative of f(x,y) with respect to x and y. f'(x,y) = In(8+x2+3y2) - In(8+x2) f'(x,y) = 8+x2+3y7 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 + x^2 + 3y^2) ; P(- 3,1); <1,1> Find the gradient of f(x,y) = ln (8 + x^2 + 3y^2) . ∇f(x,y) = < , > The directional derivative is . (Type an exact answer, using radicals as needed.)