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Practice: Directional Derivative (2)
Related Topics
Wize University Calculus 2 Textbook > Multivariable Functions
Gradient and the directional derivative
2 Activities
Calculate
D
v
⃗
f
(
x
,
y
,
z
)
D_{\vec{v}}f(x,~y,~z)~
D
v
f
(
x
,
y
,
z
)
where
f
(
x
,
y
,
z
)
=
9
x
1
3
z
1
2
+
y
10
10
f(x,~y,~z)=9x^{\frac{1}{3}}z^{\frac{1}{2}}+\frac{y^{10}}{\sqrt{10}}~
f
(
x
,
y
,
z
)
=
9
x
3
1
z
2
1
+
10
y
10
in the direction of
v
⃗
=
<
−
1
,
0
,
1
>
.
\vec{v}=~<-1,~0,~1>.
v
=
<
−
1
,
0
,
1
>
.
The directional derivative is
I don't know
Check Submission
More Gradient and the directional derivative Questions:
If
∇
f
=
(
1
,
4
)
\nabla f=\left(1,4\right)
∇
f
=
(
1
,
4
)
at a given point
P
P
P
,
a) Calculate the directional derivative of
f
(
x
,
y
)
f\left(x,y\right)
f
(
x
,
y
)
at point
P
P
P
in the direction of the vector
⟨
5
,
12
⟩
\left\langle5,12\right\rangle
⟨
5
,
12
⟩
.
b) Find a unit vector
u
⃗
\vec{u}
u
such that the directional derivative of
f
(
x
,
y
)
f\left(x,y\right)
f
(
x
,
y
)
at point
P
P
P
is zero.