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# Use implicit differentiation to find an equation of the tangent line to the curve at the given point.$x^2 + y^2 = (2x^2 + 2y^2 - x)^2, (0, \frac {1}{2}),$ (cardiod)

## $$y-\frac{1}{2}=1(x-0)$$ $$\text { or } y=x+\frac{1}{2}$$

Derivatives

Differentiation

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##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

in this problem rescues and present the transition to find the question of defensive line to the given tour at a given 0.1 Health. We know the question of one will be up for y. Minus or not is director of dysfunction of a little argument point? Excellent times explains. It's not so in order to find the question the personally to pack light or find derivative related given 40 So to do that last time David off all the perfect suspect X we have to expose to wine times why prime that is equal to two times two x ray plus, um, to Weisberg when it's X times. Now there was a look in your function, which is four X plus four. Why times y prime minus one. All right. In order to find directive at people that that given point Les Plus X not on a warning in. So we have zero plus one crime that is equal to two times zero plus one. Hell, uh, my zero. That's like by zero plus two. Y pine likes one from this. We see that Why prime is equal. One off course. This is they were to ever let that given 10.0. Now, since we know this less like what your envy have Wyman's health is a photo one Times X minus zero Promise me that when the question of friends let s x plus one.

Derivatives

Differentiation

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