implicit differentiation arctan(x^2*y)=x+x*y^2, calculus 1 tutorial | Summary and Q&A

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August 2, 2014
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implicit differentiation arctan(x^2*y)=x+x*y^2, calculus 1 tutorial

TL;DR

This video covers the process of taking derivatives using implicit differentiation and demonstrates step-by-step how to solve a specific problem.

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Questions & Answers

Q: What is implicit differentiation?

Implicit differentiation is a technique used to find derivatives of equations where it is not possible to solve explicitly for one variable in terms of the other.

Q: How is chain rule used in implicit differentiation?

In implicit differentiation, when taking the derivative of a function involving multiple variables, the chain rule is used to differentiate each term separately.

Q: What is the product rule in implicit differentiation?

The product rule states that the derivative of a product of two functions is the first function times the derivative of the second function, plus the second function times the derivative of the first function.

Q: Can implicit differentiation be used for any type of equation?

Implicit differentiation is particularly useful for equations that cannot be easily solved for one variable explicitly, such as when the equation involves trigonometric or inverse functions.

Summary & Key Takeaways

  • The content explains the process of implicit differentiation and how it is used to find derivatives.

  • It provides a detailed example of taking the derivative of a function involving inverse tangent, x, and y.

  • The video demonstrates the use of chain rule and product rule in implicit differentiation to simplify the problem.

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