Determine whether the statement is true or false. Explain your answer. In each exercise, assume that f denotes a differentiable function of two variables whose domain is the x y -plane . If v = 2 u then the directional derivative of f in the direction of v at a point x 0 , y 0 is twice the directional derivative of f in the direction of u at the point x 0 , y 0 .
Determine whether the statement is true or false. Explain your answer. In each exercise, assume that f denotes a differentiable function of two variables whose domain is the x y -plane . If v = 2 u then the directional derivative of f in the direction of v at a point x 0 , y 0 is twice the directional derivative of f in the direction of u at the point x 0 , y 0 .
Determine whether the statement is true or false. Explain your answer. In each exercise, assume that
f
denotes a differentiable function of two variables whose domain is the
x
y
-plane
.
If
v
=
2
u
then the directional derivative of
f
in the direction of
v
at a point
x
0
,
y
0
is twice the directional derivative of
f
in the direction of u at the point
x
0
,
y
0
.
Considering the following graph of the given function f.
у
The xy-coordinate plane is given. The curve enters the
window in the second quadrant nearly horizontal, goes down
and right, crosses the negative x-axis, changes direction on
the negative y-axis, goes up and right, crosses the positive
x-axis, and exits the window in the first quadrant nearly
horizontal.
Use the graph of f to complete the following table.
f(x)
f'(x)
x > 0
f(x) > 0
f'(x) ? v 0
x > 0
f(x) 0
f'(x) ? v 0
x < 0
f(x) < 0
f'(x) ? v 0
Sketch the graph of f and f' on the same coordinate axes.
y
y
y
Engineer math
Determine the Directional Derivative of:
State the rule that has to be applied first in order to differentiation the function y = -5te2t.
a.
Chain Rule
b.
Product Rule
c.
Quotient Rule
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