Basic derivative rules: find the error | Derivative rules | AP Calculus AB | Khan Academy

TL;DR

Avery and Hannah attempted to find derivatives using basic differentiation rules, but made mistakes in different steps.

Transcript

• [Voiceover] So we have two examples here of someone trying to find the derivative of an expression. On the left-hand side, it says "Avery tried to find the derivative, "of seven minus five x using basic differentiation rules. "Here is her work," and on the right-hand side it says "Hannah tried to find the derivative, "of negative three plus eight... Read More

Key Insights

• 🤘 Differentiation requires attention to detail, specifically regarding signs and the proper application of differentiation rules.
• 🥺 Mistakes can occur at any step of the differentiation process, potentially leading to incorrect final answers.
• 📏 Understanding the properties of derivatives, such as the derivative of a constant and the product rule, is crucial for accurate differentiation.

Questions & Answers

Q: What is the mistake Avery made at step one?

Avery mistakenly forgot to include the negative sign when finding the derivative of the constant term, leading to an incorrect final answer.

Q: What is the mistake Hannah made at step three?

Hannah incorrectly assumed that the derivative of a product is equal to the product of the derivatives, resulting in an incorrect final answer.

Q: Why did Avery's logic after step one still seem correct?

After Avery's mistake in step one, her logic for finding the derivative of the constant term and the first degree term remained correct, resulting in the correct partial derivatives. However, the final answer was incorrect due to the initial mistake.

Q: What is the correct way to find the derivative of a constant times an expression?

The correct way to find the derivative of a constant times an expression is to multiply the constant by the derivative of the expression. This would have provided the correct result as shown in Avery's approach.

Summary & Key Takeaways

• Avery incorrectly forgot to include the negative sign in step one when finding the derivative of the constant term.

• Hannah wrongly assumed that the derivative of a product is equal to the product of the derivatives.

• Avery correctly found the derivative of the first degree term but made the error in step one, resulting in an incorrect final answer.

• Hannah correctly found the derivative of the constant term but made the mistake in step three, leading to an incorrect final answer.