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Linear Algebra
Linear Algebra Pulse
Five questions across 8 topics. No timer.
1 / 5
Linear Algebra
Question 1 of 5
foundation (2/10)
state theorem
For a function
f
:
R
n
→
R
, define the PARTIAL DERIVATIVE
∂
f
/
∂
x
i
at a point
a
.
Hide and think first
A.
lim
h
→
0
(
f
(
a
+
h
e
i
)
−
f
(
a
))
/
h
. Hold other coordinates fixed and take a one-variable derivative in direction
e
i
.
B.
The full gradient of
f
at
a
— partials and gradient are the same vector-valued object.
C.
The directional derivative of
f
in the unit direction
a
/∥
a
∥
— the partial along the position vector.
D.
A piecewise rate of change:
(
f
(
a
+
e
i
)
−
f
(
a
))
/1
if all coordinates of
a
are non-negative, else zero.
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