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Use implicit differentiation to find an equation of the tangent line to the curve at the given point.$ \sin (x + y) = 2x - 2y, (\pi, \pi) $

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01:10

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Mitchell C.

September 30, 2020

what kind of explanation is this Frank. You did the math in your in head. Thanks for help scumbag.

Missouri State University

Campbell University

University of Michigan - Ann Arbor

Idaho State University

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.

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Use implicit differentiati…

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Find an equation of the ta…

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Find an equation of the t…

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In this problem were given a cur and we are students differentiation to find the equation of the tangent line at a given .55 to sure. We know that the equation of tangent line will be able to form y minus y, not times the arato of this function and will let that the given point x not times x, minus x, not where this is y, not- and this point is x now. So let's say derivative on both sides with respect to x and we have cosine x plus y times. Derivative of inner function to d d x of x plus y is equal to 2 minus 2 y prime, that is cosine x plus y times y prime plus 1 is equal to 2 minus 2 y prime. Let'S group, all the terms with y prime on 1 side, we have y prime 2 plus cosine x, plus y is equal to 2 minus cosine x plus y from this we can see that y prime is 2 minus cosine x, plus y divided by 2 plus Cosine x, plus y and multiply given x not, and i noted, tidy 5 prime. We see that y prime is equal to 2 minus cosine 2 pi divided by 2 plus cosine 2 pi. That is equal to 1 over 3. Now, let's apply everything into the equation of tangent land. We have y minus pi is equal to 1 third x minus pi from the speed and see that equation of tenentes 1 third of x, plus 2 pi over 3.

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