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 ∂f/∂x?

4

from “The Partial Derivative”

f = 2x + y. What is ∂f/∂x?

2

from “The Partial Derivative”

f = x² + 6y. What is ∂f/∂x?

2x

from “Computing Partial Derivatives”

f = 3x²y. What is ∂f/∂y?

3x²

from “Computing Partial Derivatives”

f = 4x³. What is ∂²f/∂x²?

24x

from “Higher Partial Derivatives”

f = 3x³. What is ∂²f/∂x²?

18x

from “Higher Partial Derivatives”

f = x³y³. What is ∂²f/∂x∂y?

9x²y²

from “The Mixed Derivative Theorem”

f = x²y³. Is ∂²f/∂x∂y equal to ∂²f/∂y∂x?

yes

from “The Mixed Derivative Theorem”

Each term multiplies ∂z/∂x by

dx/dt

from “The Chain Rule for Partial Derivatives”

dz/dt =

∂z/∂x · dx/dt + ∂z/∂y · dy/dt

from “The Chain Rule for Partial Derivatives”

f = 6x + 2y. What is ∇f?

(6, 2)

from “The Gradient Vector”

f = 3x + 5y. What is ∇f?

(3, 5)

from “The Gradient Vector”

∇f = (15, 20) 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, ∇f and ∇g are

parallel

from “Lagrange Multipliers”

The λ in ∇f = λ∇g 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”

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