Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.$ x^2 + 2xy + 4y^2 = 12, (2, 1) $ (ellipse)
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Doruk Isik
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
00:55
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 5
Implicit Differentiation
Derivatives
Differentiation
University of Nottingham
Idaho State University
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.
06:19
Use implicit differentiati…
02:34
04:03
01:23
05:00
01:37
06:23
08:56
(a) Use implicit different…
In this problem, we are asked to use efficient differentiation to find the equation of time line of the curve at a given .21 all right. We know that the equation of tangent lines will be on 1 line. An is equal to derivative of this function and will have a given point: multiplied by x, minus x, not where y not is 1 and x. Not is 2 point, so we need to find a derivative in order to do that. Less like derivative on both sides with respect to x, we have 2 x plus for this term, will be using product rule 2 y plus 2 x times y prime plus 8 y times y prime is equal to 0 and, let's pluck given x and y in Order to find derivative at this given point in order to find this term, we have 2 times 2 plus 2 times 1 plus 2 times 2 y prime plus 8 times 1 times y prime is 0 from this. We see that the y prime should be equal to negative 6 over 12 point and that is equal to negative 1 half pint. Now we have everything that we need and we can write equation of tangent line as y minus 1, which is y not times 3 overtime, negative 1, half multiplied by x, minus 2 point from this. We see that equation of the tangent line is that 2 minus x over 2.
View More Answers From This Book
Find Another Textbook
02:07
Explain how the value of the median is determined for a data set that conta…
02:10
How are the relative frequencies and percentages of categories obtained from…
04:41
The following data give the results of a sample survey. The letters $\mathrm…
00:40
Briefly explain the difference between a census and a sample survey. Why is…
03:24
Which of the three measures of central tendency (the mean, the median, and …
03:00
Explain whether each of the following constitutes a population or a sample.<…
00:58
it possible for a (quantitative) data set to have no mean, no median, or no…
03:49
Thirty adults were asked which of the following conveniences they would find…
05:34
Two students are randomly selected from a statistics class, and it is observ…
01:18
The following table gives the state taxes (in dollars) on a pack of cigarett…