# Sect 4 9 #5 Intro to Antiderivative & Backward Power Rule | Summary and Q&A

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January 29, 2015
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blackpenredpen
Sect 4 9 #5 Intro to Antiderivative & Backward Power Rule

## TL;DR

Learn how to find the antiderivative of a polynomial function using the backward power rule, which reverses the steps of the power rule.

## Key Insights

• ◀️ Antiderivatives involve finding the derivative backward.
• ✊ The backward power rule is used to find the antiderivative of polynomial functions.
• ✊ The regular power rule is used to find derivatives.
• ✊ Adding one to the exponent and dividing by the new exponent is part of the backward power rule for antiderivatives.
• 😀 The antiderivative includes a constant term (represented as "+ C").
• ✊ The backward power rule reverses the operations of the regular power rule.
• 🗂️ The antiderivative of x to the n power is x to the n plus one divided by n plus one.

## Transcript

we are going to find anti-derivative for the function f of x is equal to x plus 1 times 2x minus 1. for antiderivative this just means that we are going to do the derivative backwards however here we have a polynomial times another polynomial so in this situation it doesn't matter if you want to do the regular derivative with the derivative backwar... Read More

### Q: What is the difference between finding a derivative and finding an antiderivative?

Finding a derivative involves taking the derivative backward, while finding an antiderivative involves reversing the derivative process.

### Q: How do you apply the regular power rule for derivatives?

For x to the n power, the derivative is n times x to the n minus one.

### Q: When should the backward power rule be used?

The backward power rule should be used when finding the antiderivative of a polynomial function.

### Q: How can the backward power rule be applied to find the antiderivative of a polynomial function?

To find the antiderivative, add one to the exponent and divide by the new exponent for each term in the polynomial function.

## Summary & Key Takeaways

• Antiderivatives involve finding the derivative backward, and for polynomial functions, the backward power rule is used.

• The regular power rule for derivatives involves bringing the exponent to the front and subtracting one.

• The backward power rule for antiderivatives involves adding one to the exponent and dividing by the new exponent.