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Find $ dy/dx $ by implicit differentiation.$ x^3 - xy^2 + y^3 = 1 $

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00:37

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Oregon State 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.

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In this problem were given an equation and were asked to use implicit differentiation to find directoirespect x, we're going to take the ritual the terms with respect to x, leesome first term, that is 3 x squared minus 4, the second term we're going to use for a Rule so we have y square plus x times that is first term multiplied by the root of second term, which is 2 y times dy dx since y is a function f x plus we have 3 y stay d x again, since 1 is contrax right hand, Side is 0, since 1 is just ascent. So let's report the terms with t y d x on left hand, side dividex of 3 y squared minus. We have 2 x y plus write old terms without dyd on the right hand side. So we have y squared minus 3 x. Squared from this we can see that the rot of point with respect to x is equal to 1 squared minus 3 x divided by well. Why is it common variable, so we can write this 1. As y times 3 y minus 2 x,

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