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Time

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Use implicit differentiation to find the derivative of a function

Use implicit differentiation to find $\frac{dy}{dx}$ if $7x^2+14y^2=121$ .

$\frac{-x}{2y}$

$\frac{x}{y}$

$\frac{-x}{y}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=7x^2-3y^2$ .

$\frac{2x+y}{\left[1-x-y\right]}$

$\frac{14x}{\left[1-6y\right]}$

$\frac{2x+y}{\left[1-x-6y\right]}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $x^3+y^2=0$ .

$\frac{-3x^2}{\left[2y\right]}$

$\frac{x^3-xy}{\left[x^2-3y^2\right]}$

$\frac{x^3-6xy}{\left[x^2-3y^2\right]}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=3x^2-2y$ .

$x^2$

$\frac{x}{\left[1+9e^y\right]}$

$2x$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=2x^2-5e^y$ .

$\frac{10x}{\left[1+9e^y\right]}$

$\frac{x}{\left[1+9e^y\right]}$

$\frac{4x}{\left[1+5e^y\right]}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=15x^2+5x-4y$ .

$2x+2$

$\frac{x}{\left[1+9e^y\right]}$

$6x+1$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=10x^2-4y$ .

$4x$

$\frac{x}{\left[1+9e^y\right]}$

$2x^3$

Use implicit differentiation to find $\frac{dy}{dx}$ if $x^3+y^3=7$ .

$\frac{-x^2}{y^2}$

$\frac{x}{y}$

$\frac{-x}{y}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=\left(3x\right)$ .

$\frac{1}{\sqrt{1+9x^2}}$

$\frac{6x}{y}$

$\frac{1}{\sqrt{1-9x^2}}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $x^4+y^2=49$ .

$\frac{-3x^2}{2y}$

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

$\frac{-2x^3}{y}$

Questions

Time

Score

Use implicit differentiation to find the derivative of a function

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿7x2+14y2=1217x^2+14y^2=1217x2+14y2=121﻿.

﻿−x2y\frac{-x}{2y}2y−x​﻿

﻿xy\frac{x}{y}yx​﻿

﻿−xy\frac{-x}{y}y−x​﻿

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿y=7x2−3y2y=7x^2-3y^2y=7x2−3y2﻿.

﻿2x+y[1−x−y]\frac{2x+y}{\left[1-x-y\right]}[1−x−y]2x+y​﻿

﻿14x[1−6y]\frac{14x}{\left[1-6y\right]}[1−6y]14x​﻿

﻿2x+y[1−x−6y]\frac{2x+y}{\left[1-x-6y\right]}[1−x−6y]2x+y​﻿

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿x3+y2=0x^3+y^2=0x3+y2=0﻿.

﻿−3x2[2y]\frac{-3x^2}{\left[2y\right]}[2y]−3x2​﻿

﻿x3−xy[x2−3y2]\frac{x^3-xy}{\left[x^2-3y^2\right]}[x2−3y2]x3−xy​﻿

﻿x3−6xy[x2−3y2]\frac{x^3-6xy}{\left[x^2-3y^2\right]}[x2−3y2]x3−6xy​﻿

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿y=3x2−2yy=3x^2-2yy=3x2−2y﻿.

﻿x2x^2x2﻿

﻿x[1+9ey]\frac{x}{\left[1+9e^y\right]}[1+9ey]x​﻿

﻿2x2x2x﻿

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿y=2x2−5eyy=2x^2-5e^yy=2x2−5ey﻿.

﻿10x[1+9ey]\frac{10x}{\left[1+9e^y\right]}[1+9ey]10x​﻿

﻿x[1+9ey]\frac{x}{\left[1+9e^y\right]}[1+9ey]x​﻿

﻿4x[1+5ey]\frac{4x}{\left[1+5e^y\right]}[1+5ey]4x​﻿

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿y=15x2+5x−4yy=15x^2+5x-4yy=15x2+5x−4y﻿.

﻿2x+22x+22x+2﻿

﻿x[1+9ey]\frac{x}{\left[1+9e^y\right]}[1+9ey]x​﻿

﻿6x+16x+16x+1﻿

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿y=10x2−4yy=10x^2-4yy=10x2−4y﻿.

﻿4x4x4x﻿

﻿x[1+9ey]\frac{x}{\left[1+9e^y\right]}[1+9ey]x​﻿

﻿2x32x^32x3﻿

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿x3+y3=7x^3+y^3=7x3+y3=7﻿.

﻿−x2y2\frac{-x^2}{y^2}y2−x2​﻿

﻿xy\frac{x}{y}yx​﻿

﻿−xy\frac{-x}{y}y−x​﻿

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿y=(3x)y=\left(3x\right)y=(3x)﻿.

﻿11+9x2\frac{1}{\sqrt{1+9x^2}}1+9x2​1​﻿

﻿6xy\frac{6x}{y}y6x​﻿

﻿11−9x2\frac{1}{\sqrt{1-9x^2}}1−9x2​1​﻿

Use implicit differentiation to find ﻿dydx\frac{dy}{dx}dxdy​﻿ if ﻿x4+y2=49x^4+y^2=49x4+y2=49﻿﻿.

﻿−3x22y\frac{-3x^2}{2y}2y−3x2​﻿

﻿3x22y\frac{3x^2}{2y}2y3x2​﻿

﻿−2x3y\frac{-2x^3}{y}y−2x3​﻿

Incorrect

Great!

Use implicit differentiation to find $\frac{dy}{dx}$ if $7x^2+14y^2=121$ .

$\frac{-x}{2y}$

$\frac{x}{y}$

$\frac{-x}{y}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=7x^2-3y^2$ .

$\frac{2x+y}{\left[1-x-y\right]}$

$\frac{14x}{\left[1-6y\right]}$

$\frac{2x+y}{\left[1-x-6y\right]}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $x^3+y^2=0$ .

$\frac{-3x^2}{\left[2y\right]}$

$\frac{x^3-xy}{\left[x^2-3y^2\right]}$

$\frac{x^3-6xy}{\left[x^2-3y^2\right]}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=3x^2-2y$ .

$x^2$

$\frac{x}{\left[1+9e^y\right]}$

$2x$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=2x^2-5e^y$ .

$\frac{10x}{\left[1+9e^y\right]}$

$\frac{x}{\left[1+9e^y\right]}$

$\frac{4x}{\left[1+5e^y\right]}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=15x^2+5x-4y$ .

$2x+2$

$\frac{x}{\left[1+9e^y\right]}$

$6x+1$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=10x^2-4y$ .

$4x$

$\frac{x}{\left[1+9e^y\right]}$

$2x^3$

Use implicit differentiation to find $\frac{dy}{dx}$ if $x^3+y^3=7$ .

$\frac{-x^2}{y^2}$

$\frac{x}{y}$

$\frac{-x}{y}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $y=\left(3x\right)$ .

$\frac{1}{\sqrt{1+9x^2}}$

$\frac{6x}{y}$

$\frac{1}{\sqrt{1-9x^2}}$

Use implicit differentiation to find $\frac{dy}{dx}$ if $x^4+y^2=49$ .

$\frac{-3x^2}{2y}$

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

$\frac{-2x^3}{y}$