delta y vs. dy (differential) | Summary and Q&A

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August 1, 2018
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blackpenredpen
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delta y vs. dy (differential)

TL;DR

This video explains the difference between Delta Y and dy in calculus, using the example of the square root of x function.

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Questions & Answers

Q: What is the difference between Delta Y and dy?

Delta Y represents the exact change in Y values, while dy is an approximated change in Y values using derivatives.

Q: How do you calculate Delta Y and dy?

To calculate Delta Y, subtract the initial Y value from the final Y value. To calculate dy, multiply the derivative of the function by the change in X values.

Q: Why is dy an approximation?

dy is an approximation because it uses the derivative of the function to estimate the change in Y values. It is not as precise as Delta Y, which represents the actual change.

Q: How does the concept of differentials come into play?

Differentials, represented by dy and dx, are used to approximate the change in Y and X values respectively. They allow for a more accurate estimation of changes in calculus.

Summary & Key Takeaways

  • The video demonstrates the concept of Delta Y and dy by using the square root of x function.

  • It shows how to calculate the exact change in Y values (Delta Y) and the approximated change in Y values (dy) using calculus.

  • The video highlights the importance of using derivatives to approximate the change in Y values and explains the concept of differentials.

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