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If $ x^2 + xy + y^3 = 1, $ find the value of $ y" $ at the point where $ x = 1. $

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02:07

Frank Lin

03:18

Doruk Isik

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Catherine A.

October 23, 2020

Finally, now Im done with my homework

I've been struggling with Calculus: Early Transcendentals, this is so helpful

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

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.

0:00

If $ x^2 + xy + y^3 = 1, $…

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If $x^{2}+x y+y^{3}=1,$ fi…

03:47

If $x y+y^{2}=1,$ find the…

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If $y=\frac{1}{x}+\frac{2}…

00:47

If $y=\frac{1}{x}+\frac{2…

here we want to do some implicit differentiation. Um And this is going to be X squared plus X. Y. That's why cubed equals one. And we want to find why triple crime at the point where X equals one. So do you this we're going to have X squared. Um Why? And then we're going to have yeah. Um This is uh two x plus and then we're gonna want to do chain rule here. So we end up getting um the derivative of the first one acts so times why? Plus X. Why primed? And then we'll have plus free Y squared. Why prime equal to zero. And then we can keep doing this. And when we evaluated at X equals one, we ended up seeing that 42 is the final answer.

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