Implicit Differentiation - Find The First & Second Derivatives | Summary and Q&A

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October 21, 2018
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The Organic Chemistry Tutor
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Implicit Differentiation - Find The First & Second Derivatives

TL;DR

Implicit differentiation is a technique used to find the derivative of an equation with both x and y variables.

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Questions & Answers

Q: What is implicit differentiation?

Implicit differentiation is a method used to find the derivative of an equation with both x and y variables. It involves differentiating both sides of the equation with respect to x, treating y as a function of x.

Q: How do you differentiate terms with x variables?

To differentiate terms with x variables, the power rule is used. For example, the derivative of x^2 is 2x.

Q: How do you differentiate terms with y variables?

When differentiating terms with y variables, dy/dx is added to the equation. For example, the derivative of y^3 is 3y^2 * dy/dx.

Q: How do you isolate dy/dx after differentiation?

To isolate dy/dx, factors without dy/dx are moved to the other side of the equation. Then, dy/dx is factored out and divided by the remaining terms.

Summary & Key Takeaways

  • Implicit differentiation involves differentiating both sides of an equation with respect to x, treating y as a function of x.

  • The power rule is used to differentiate terms with x variables, and dy/dx is added to terms with y variables.

  • After differentiating, factors without dy/dx are moved to the other side of the equation, and dy/dx is factored out to isolate it.

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