Partial Derivatives flashcards
22 practice cards drawn from the Partial Derivatives lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
Read the Partial Derivatives lessons in full →
f = 4x + y. What is ?
4
from “The Partial Derivative”
f = 2x + y. What is ?
2
from “The Partial Derivative”
. What is ?
2x
from “Computing Partial Derivatives”
. What is ?
from “Computing Partial Derivatives”
. What is ?
24x
from “Higher Partial Derivatives”
. What is ?
18x
from “Higher Partial Derivatives”
. What is ?
from “The Mixed Derivative Theorem”
. Is equal to ?
yes
from “The Mixed Derivative Theorem”
Each term multiplies by
from “The Chain Rule for Partial Derivatives”
from “The Chain Rule for Partial Derivatives”
f = 6x + 2y. What is ?
(6, 2)
from “The Gradient Vector”
f = 3x + 5y. What is ?
(3, 5)
from “The Gradient Vector”
and the unit step u = (0.6, 0.8). What is the slope along u?
25
from “Directional Derivatives”
Walking at right angles to the gradient, the slope is
0
from “Directional Derivatives”
A tangent plane is fixed by
the two partial derivatives
from “Tangent Planes”
A tangent plane is built at
one chosen point
from “Tangent Planes”
A surface is stationary where
both partials are zero
from “Stationary Points of a Surface”
Rising in x and falling in y at a level point is a
saddle
from “Stationary Points of a Surface”
At a constrained optimum, and are
parallel
from “Lagrange Multipliers”
The in is called the
multiplier
from “Lagrange Multipliers”
The double integral is written as
two signs, one per direction
from “The Volume Under a Surface”
Each fixed-y slice of the solid is
an area under a curve
from “The Volume Under a Surface”