Find the directional derivative of f at P in the direction of a vector making the counterclockwise angle θ with the positive x -axis . f x , y , = tan 2 x + y ; P π / 6 , π / 3 ; θ = 7 π / 4
Find the directional derivative of f at P in the direction of a vector making the counterclockwise angle θ with the positive x -axis . f x , y , = tan 2 x + y ; P π / 6 , π / 3 ; θ = 7 π / 4
Find the directional derivative of
f
at
P
in the direction of a vector making the counterclockwise angle
θ
with the positive
x
-axis
.
f
x
,
y
,
=
tan
2
x
+
y
;
P
π
/
6
,
π
/
3
;
θ
=
7
π
/
4
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.
Find the directional derivative of the function
pez(x, y) = cos(2x) In (5y) + sin ¹(3x) (1-²)¹/2
at the point P(0, 1/2) in the direction of the vector a = i + j√2.
Present your answer in the exact form (don't use a calculator).
Find the angle between vector a and x-axis in degrees up to two decimal places.
Hint: Recall that sin¹x is the inverse function with respect to function sin.x.
Find the directional derivative of f at the given point in the direction indicated by the given angle Theta. (Note: Theta is the angle the direction vector u makes with the positive x-axis so the components of u are [cosine (Theta) , sine (Theta)]
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