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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)

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01:32

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Campbell University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

09:41

Use implicit differentiati…

01:23

02:50

Find all points on the cur…

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.

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