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Mathematics

9th Grade

Used 2+ times

WS_Calc_3.2_Implicit.Diff
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20 questions

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1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the derivative dydx\frac{dy}{dx} for exy=x−ye^{xy} = x - y using implicit differentiation.

yexyxexy−1\frac{ye^{xy}}{xe^{xy} - 1}

exyx−y\frac{e^{xy}}{x - y}

xexyy−x\frac{xe^{xy}}{y - x}

1−xy+y21−xy+x2\frac{1-xy+y^2}{1-xy+x^2}

2.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Differentiate y3+3x2=12y^3 + 3x^2 = 12 implicitly to find dydx\frac{dy}{dx} .

2x3\frac{2x}{3}

3y22x\frac{3y^2}{2x}

−2xy2\frac{-2x}{y^2}

−32x\frac{-3}{2x}

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Use implicit differentiation to find dydx\frac{dy}{dx} for xy2=7xy^2 = 7 .

2yx\frac{2y}{x}

−2yx\frac{-2y}{x}

−y2x\frac{-y}{2x}

x2y\frac{x}{2y}

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find dydx\frac{dy}{dx} by implicitly differentiating ln⁡(xy)=x2\ln(xy) = x^2 .

12xy−1\frac{1}{2xy-1}

2xy−yx2xy-\frac{y}{x}

yy−2x\frac{y}{y-2x}

2xy\frac{2x}{y}

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Differentiate x2+4xy+y2=8x^2 + 4xy + y^2 = 8 implicitly to find dydx\frac{dy}{dx} .

x+2yx+4y\frac{x+2y}{x+4y}

−2x+yx+y\frac{-2x+y}{x+y}

−2y+xy+2x-\frac{2y+x}{y+2x}

−x+2yx+4y-\frac{x+2y}{x+4y}

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find dydx\frac{dy}{dx} for cos⁡(xy)=x−y\cos(xy) = x - y using implicit differentiation.

−ysin⁡(xy)+1xsin⁡(xy)−1-\frac{y\sin(xy)+1}{x\sin(xy)-1}

y−1sin⁡(xy)\frac{y-1}{\sin(xy)}

ysin⁡(xy)−1sin⁡(xy)+1\frac{y \sin(xy)-1}{\sin(xy)+1}

1−ysin⁡(xy)1+sin⁡(xy)\frac{1-y \sin(xy)}{1+\sin(xy)}

7.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Use implicit differentiation to find dydx\frac{dy}{dx} for x3+y3=6xyx^3 + y^3 = 6xy .

x2+y22x+2y\frac{x^2 + y^2}{2x + 2y}

2x2−y2x−2y\frac{2x^2 - y^2}{x - 2y}

x−yx2−y2\frac{x - y}{x^2 - y^2}

−2y−x22x−y2-\frac{2y-x^2}{2x-y^2}

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