Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given vector . Be sure to use a unit vector for the direction vector. 21 f ( x , y ) = 4 − x 2 − 2 y ; P ( 2 , − 2 ) ; 〈 1 5 , 2 5 〉
Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given vector . Be sure to use a unit vector for the direction vector. 21 f ( x , y ) = 4 − x 2 − 2 y ; P ( 2 , − 2 ) ; 〈 1 5 , 2 5 〉
Solution Summary: The author calculates the directional derivative of the function f(x,y,)=sqrt4-x2-2y at the point P (2,
Computing directional derivatives with the gradientCompute the directional derivative of the following functions at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector.
21
f
(
x
,
y
)
=
4
−
x
2
−
2
y
;
P
(
2
,
−
2
)
;
〈
1
5
,
2
5
〉
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector.
g(x, y) = ln (4 + x2 + y2); g(-1, 2); ⟨2, 1⟩
Derivative of vector functions Compute the derivative of the followingfunctions.a. r(t) = ⟨t3, 3t2, t3/6⟩ b. r(t) = e-t i + 10√t j + 2 cos 3t k
Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector.
h(x, y) = e-x - y; P(ln 2, ln 3); ⟨1, 1⟩
Chapter 15 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
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