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Time

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Understanding differential

Is the sentence true or false?
Given a function y=f(x), df = ydx

True

False

Compute the differential for y=sint

$\left(\cos t\right)dt$

$\left(\sin t\right)dt$

Is the sentence true or false?
For function f(x), df = f’(x)dx

True

False

Is the sentence true or false?
The differential is another name for the Jacobian matrix of partial derivatives

True

False

Is the sentence true or false?
The differential dx represents an infinitely small change in the variable x

True

False

Compute the differential for $y=\cos2x$

$\left(\sin2x\right)dx$

$\left(-2\sin2x\right)dx$

Fill in the blank:
Given a function y=f(x), then dy=___________

dx

f'(x)dx

f'(y)dx

Compute the differential for y=e^t

e^t

e^tdt

Compute the differential for $y=t^3-4t^2+7t$

$\left(3t^2-8t+7\right)dt$

$\left(3t^2-4t+7\right)dx$

Is the sentence true or false?
The term differential refers to an infinitesimal ("infinitely small") change in some varying quantity

True

False

Questions

Time

Score

Understanding differential

Is the sentence true or false?
Given a function y=f(x), df = ydx

True

False

Compute the differential for y=sint

$\left(\cos t\right)dt$

$\left(\sin t\right)dt$

Is the sentence true or false?
For function f(x), df = f’(x)dx

True

False

Is the sentence true or false?
The differential is another name for the Jacobian matrix of partial derivatives

True

False

Is the sentence true or false?
The differential dx represents an infinitely small change in the variable x

True

False

Compute the differential for $y=\cos2x$

$\left(\sin2x\right)dx$

$\left(-2\sin2x\right)dx$

Fill in the blank:
Given a function y=f(x), then dy=___________

dx

f'(x)dx

f'(y)dx

Compute the differential for y=e^t

e^t

e^tdt

Compute the differential for $y=t^3-4t^2+7t$

$\left(3t^2-8t+7\right)dt$

$\left(3t^2-4t+7\right)dx$

Is the sentence true or false?
The term differential refers to an infinitesimal ("infinitely small") change in some varying quantity

True

False

Incorrect

Great!

Questions

Time

Score

Understanding differential

Is the sentence true or false?Given a function y=f(x), df = ydx

True

False

Compute the differential for y=sint

﻿(cos⁡t)dt\left(\cos t\right)dt(cost)dt﻿

﻿(sin⁡t)dt\left(\sin t\right)dt(sint)dt﻿

Is the sentence true or false?For function f(x), df = f’(x)dx

True

False

Is the sentence true or false?The differential is another name for the Jacobian matrix of partial derivatives

True

False

Is the sentence true or false?The differential dx represents an infinitely small change in the variable x

True

False

Compute the differential for ﻿y=cos⁡2xy=\cos2xy=cos2x﻿

﻿(sin⁡2x)dx\left(\sin2x\right)dx(sin2x)dx﻿

﻿(−2sin⁡2x)dx\left(-2\sin2x\right)dx(−2sin2x)dx﻿

Fill in the blank:Given a function y=f(x), then dy=___________

dx

f'(x)dx

f'(y)dx

Compute the differential for y=et

et

etdt

Compute the differential for ﻿y=t3−4t2+7ty=t^3-4t^2+7ty=t3−4t2+7t﻿

﻿(3t2−8t+7)dt\left(3t^2-8t+7\right)dt(3t2−8t+7)dt﻿

﻿(3t2−4t+7)dx\left(3t^2-4t+7\right)dx(3t2−4t+7)dx﻿

Is the sentence true or false?The term differential refers to an infinitesimal ("infinitely small") change in some varying quantity

True

False

Incorrect

Great!

Is the sentence true or false?
Given a function y=f(x), df = ydx

$\left(\cos t\right)dt$

$\left(\sin t\right)dt$

Is the sentence true or false?
For function f(x), df = f’(x)dx

Is the sentence true or false?
The differential is another name for the Jacobian matrix of partial derivatives

Is the sentence true or false?
The differential dx represents an infinitely small change in the variable x

Compute the differential for $y=\cos2x$

$\left(\sin2x\right)dx$

$\left(-2\sin2x\right)dx$

Fill in the blank:
Given a function y=f(x), then dy=___________

Compute the differential for y=e^t

e^t

e^tdt

Compute the differential for $y=t^3-4t^2+7t$

$\left(3t^2-8t+7\right)dt$

$\left(3t^2-4t+7\right)dx$

Is the sentence true or false?
The term differential refers to an infinitesimal ("infinitely small") change in some varying quantity