How to Compute Delta y and the Differential dy | Summary and Q&A

TL;DR

This video explains how to compute differentials and approximations using formulas and an example function.

Key Insights

• 💻 Differentials can be computed using the derivative of a function and the change in X.
• 🐞 The formula for dy is dy = f'(X) * DX, where f'(X) is the derivative of the function and DX is the change in X.
• 🇾🇪 The formula for Delta Y is Delta Y = f(X + Delta X) - f(X), where Delta X is the change in X and f(X) is the original function.
• 💱 Calculating the actual change in Y provides a more accurate result than the approximation.
• 😀 The example function y = x^4 + 6 is used to demonstrate the calculations.
• ☺️ Both positive and negative values of X can be used in the formulas, depending on the context of the problem.
• 🤝 It is important to consider decimal places when dealing with calculations involving derivatives and approximations.

Transcript

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Questions & Answers

Q: What is the formula for computing dy?

The formula for computing dy is dy = f'(X) * DX, where f'(X) is the derivative of the function and DX is the change in X.

Q: How can Delta Y be calculated?

Delta Y can be calculated using the formula Delta Y = f(X + Delta X) - f(X), where f(X) is the original function and Delta X is the change in X.

Q: What is the specific example function used in the video?

The specific example function used in the video is y = x^4 + 6.

Q: What is the difference between the approximation (dy) and the actual change (Delta Y)?

The approximation (dy) provides an estimated change in Y based on the derivative, while the actual change (Delta Y) calculates the precise change in Y using the function itself.

Summary & Key Takeaways

• The video demonstrates how to compute dy and Delta Y using the formulas dy = f'(X) * DX and Delta Y = f(X + Delta X) - f(X).

• A specific example function, y = x^4 + 6, is used to illustrate the calculations.

• The video provides both the approximation (dy) and the actual change (Delta Y) in Y, which is equal to -0.004 and -0.0394 respectively.